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Overview: 1 questions will be solved this time.Among them
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation 3/(1+5%)+3*(1+1%)/(1+5%)^2+3*(1+1%)^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8 .
Question type: Mathematical calculation
Solution:
3/(1+5%)+3*(1+1%)/(1+5%)^2+3*(1+1%)^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*(1+1%)/(1+5%)^2+3*(1+1%)^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/(1+5%)^2+3*(1+1%)^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*(1+1%)^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+3.03/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+3.0603/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+3.090903/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+3.121812/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+3.15303/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+2.35284+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+2.35284+3.18456/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+2.35284+2.263207+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+2.35284+2.263207+3.216406/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+2.35284+2.263207+2.17699
=5.605442+2.643602+2.542894+2.446021+2.35284+2.263207+2.17699
=8.249044+2.542894+2.446021+2.35284+2.263207+2.17699
=10.791938+2.446021+2.35284+2.263207+2.17699
=13.237959+2.35284+2.263207+2.17699
=15.590799+2.263207+2.17699
=17.854006+2.17699
=20.030996
Answer:3/(1+5%)+3*(1+1%)/(1+5%)^2+3*(1+1%)^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8=20.030996
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation 3/(1+5%)+3*(1+1%)/(1+5%)^2+3*(1+1%)^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8 .
Question type: Mathematical calculation
Solution:
3/(1+5%)+3*(1+1%)/(1+5%)^2+3*(1+1%)^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*(1+1%)/(1+5%)^2+3*(1+1%)^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/(1+5%)^2+3*(1+1%)^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*(1+1%)^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*(1+1%)^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/(1+5%)^8
=3/1.05+3*1.01/1.05^2+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.01^2/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.05^3+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.01^3/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.05^4+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.01^4/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.05^5+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.01^5/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.05^6+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.01^6/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.05^7+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.01^7/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.05^8
=3/1.05+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+3*1.01/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+3.03/1.1025+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+3*1.0201/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+3.0603/1.157625+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+3*1.030301/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+3.090903/1.21550625+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+3*1.04060401/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+3.121812/1.2762815625+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+3*1.0510100501/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+3.15303/1.340095640625+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+2.35284+3*1.061520150601/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+2.35284+3.18456/1.40710042265625+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+2.35284+2.263207+3*1.07213535210701/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+2.35284+2.263207+3.216406/1.477455443789063
=2.857143+2.748299+2.643602+2.542894+2.446021+2.35284+2.263207+2.17699
=5.605442+2.643602+2.542894+2.446021+2.35284+2.263207+2.17699
=8.249044+2.542894+2.446021+2.35284+2.263207+2.17699
=10.791938+2.446021+2.35284+2.263207+2.17699
=13.237959+2.35284+2.263207+2.17699
=15.590799+2.263207+2.17699
=17.854006+2.17699
=20.030996
Answer:3/(1+5%)+3*(1+1%)/(1+5%)^2+3*(1+1%)^2/(1+5%)^3+3*(1+1%)^3/(1+5%)^4+3*(1+1%)^4/(1+5%)^5+3*(1+1%)^5/(1+5%)^6+3*(1+1%)^6/(1+5%)^7+3*(1+1%)^7/(1+5%)^8=20.030996