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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+1%)^6/(1+5%)^36+3*(1+1%)^7/(1+5%)^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40 .
Question type: Mathematical calculation
Solution:
3*(1+1%)^6/(1+5%)^36+3*(1+1%)^7/(1+5%)^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/(1+5%)^36+3*(1+1%)^7/(1+5%)^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*(1+1%)^7/(1+5%)^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/(1+5%)^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*1.01^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*1.01^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*1.01^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/1.05^36+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/1.05^37+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/1.05^38+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=3.18456/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+3.216406/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+0.528892+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+0.528892+3.24857/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+0.528892+0.508743+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+0.528892+0.508743+3.281056/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+0.528892+0.508743+0.489363+3*1.104622125411205/7.039988712124658
=0.549838+0.528892+0.508743+0.489363+3.313866/7.039988712124658
=0.549838+0.528892+0.508743+0.489363+0.47072
=1.07873+0.508743+0.489363+0.47072
=1.587473+0.489363+0.47072
=2.076836+0.47072
=2.547556
Answer:3*(1+1%)^6/(1+5%)^36+3*(1+1%)^7/(1+5%)^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40=2.547556
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation 3*(1+1%)^6/(1+5%)^36+3*(1+1%)^7/(1+5%)^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40 .
Question type: Mathematical calculation
Solution:
3*(1+1%)^6/(1+5%)^36+3*(1+1%)^7/(1+5%)^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/(1+5%)^36+3*(1+1%)^7/(1+5%)^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*(1+1%)^7/(1+5%)^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/(1+5%)^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*1.01^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*1.01^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*(1+1%)^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*1.01^10/(1+5%)^40
=3*1.01^6/1.05^36+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/1.05^36+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.01^7/1.05^37+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/1.05^37+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.01^8/1.05^38+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/1.05^38+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.01^9/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/1.05^39+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.01^10/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/1.05^40
=3*1.061520150601/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=3.18456/5.791816135971869+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+3*1.07213535210701/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+3.216406/6.081406942770463+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+0.528892+3*1.08285670562808/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+0.528892+3.24857/6.385477289908986+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+0.528892+0.508743+3*1.093685272684361/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+0.528892+0.508743+3.281056/6.704751154404436+3*1.104622125411205/7.039988712124658
=0.549838+0.528892+0.508743+0.489363+3*1.104622125411205/7.039988712124658
=0.549838+0.528892+0.508743+0.489363+3.313866/7.039988712124658
=0.549838+0.528892+0.508743+0.489363+0.47072
=1.07873+0.508743+0.489363+0.47072
=1.587473+0.489363+0.47072
=2.076836+0.47072
=2.547556
Answer:3*(1+1%)^6/(1+5%)^36+3*(1+1%)^7/(1+5%)^37+3*(1+1%)^8/(1+5%)^38+3*(1+1%)^9/(1+5%)^39+3*(1+1%)^10/(1+5%)^40=2.547556