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Current location：Mathematical operation > History of Mathematical Computation > Answer
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%)^30+3*(1+1%)/(1+5%)^31+3*(1+1%)^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35 .
Question type: Mathematical calculation
Solution:
3/(1+5%)^30+3*(1+1%)/(1+5%)^31+3*(1+1%)^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*(1+1%)/(1+5%)^31+3*(1+1%)^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/(1+5%)^31+3*(1+1%)^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*(1+1%)^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*1.01^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*1.01^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/1.05^32+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/1.05^33+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+3.03/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+3.0603/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+0.642253+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+0.642253+3.090903/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+0.642253+0.617787+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+0.642253+0.617787+3.121812/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+0.642253+0.617787+0.594252+3*1.0510100501/5.516015367592257
=0.694132+0.667689+0.642253+0.617787+0.594252+3.15303/5.516015367592257
=0.694132+0.667689+0.642253+0.617787+0.594252+0.571614
=1.361821+0.642253+0.617787+0.594252+0.571614
=2.004074+0.617787+0.594252+0.571614
=2.621861+0.594252+0.571614
=3.216113+0.571614
=3.787727
Answer:3/(1+5%)^30+3*(1+1%)/(1+5%)^31+3*(1+1%)^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35=3.787727
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation 3/(1+5%)^30+3*(1+1%)/(1+5%)^31+3*(1+1%)^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35 .
Question type: Mathematical calculation
Solution:
3/(1+5%)^30+3*(1+1%)/(1+5%)^31+3*(1+1%)^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*(1+1%)/(1+5%)^31+3*(1+1%)^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/(1+5%)^31+3*(1+1%)^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*(1+1%)^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*1.01^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*(1+1%)^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*1.01^5/(1+5%)^35
=3/1.05^30+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/1.05^31+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.01^2/1.05^32+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/1.05^32+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.01^3/1.05^33+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/1.05^33+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.01^4/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/1.05^34+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.01^5/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/1.05^35
=3/4.321942375150668+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+3*1.01/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+3.03/4.538039493908201+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+3*1.0201/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+3.0603/4.764941468603611+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+0.642253+3*1.030301/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+0.642253+3.090903/5.003188542033792+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+0.642253+0.617787+3*1.04060401/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+0.642253+0.617787+3.121812/5.253347969135482+3*1.0510100501/5.516015367592257
=0.694132+0.667689+0.642253+0.617787+0.594252+3*1.0510100501/5.516015367592257
=0.694132+0.667689+0.642253+0.617787+0.594252+3.15303/5.516015367592257
=0.694132+0.667689+0.642253+0.617787+0.594252+0.571614
=1.361821+0.642253+0.617787+0.594252+0.571614
=2.004074+0.617787+0.594252+0.571614
=2.621861+0.594252+0.571614
=3.216113+0.571614
=3.787727
Answer:3/(1+5%)^30+3*(1+1%)/(1+5%)^31+3*(1+1%)^2/(1+5%)^32+3*(1+1%)^3/(1+5%)^33+3*(1+1%)^4/(1+5%)^34+3*(1+1%)^5/(1+5%)^35=3.787727