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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%)^11/(1+5%)^12+3*(1+1%)^12/(1+5%)^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15 .
Question type: Mathematical calculation
Solution:
3*(1+1%)^11/(1+5%)^12+3*(1+1%)^12/(1+5%)^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/(1+5%)^12+3*(1+1%)^12/(1+5%)^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/1.05^12+3*(1+1%)^12/(1+5%)^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/1.05^12+3*1.01^12/(1+5%)^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/1.05^12+3*1.01^12/1.05^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/1.05^12+3*1.01^12/1.05^13+3*1.01^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/1.05^12+3*1.01^12/1.05^13+3*1.01^13/1.05^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/1.05^12+3*1.01^12/1.05^13+3*1.01^13/1.05^14+3*1.01^14/(1+5%)^15
=3*1.01^11/1.05^12+3*1.01^12/1.05^13+3*1.01^13/1.05^14+3*1.01^14/1.05^15
=3*1.115668346665317/1.05^12+3*1.01^12/1.05^13+3*1.01^13/1.05^14+3*1.01^14/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.01^12/1.05^13+3*1.01^13/1.05^14+3*1.01^14/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.12682503013197/1.05^13+3*1.01^13/1.05^14+3*1.01^14/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.12682503013197/1.885649142323237+3*1.01^13/1.05^14+3*1.01^14/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.12682503013197/1.885649142323237+3*1.13809328043329/1.05^14+3*1.01^14/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.12682503013197/1.885649142323237+3*1.13809328043329/1.979931599439399+3*1.01^14/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.12682503013197/1.885649142323237+3*1.13809328043329/1.979931599439399+3*1.149474213237623/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.12682503013197/1.885649142323237+3*1.13809328043329/1.979931599439399+3*1.149474213237623/2.078928179411369
=3.347005/1.79585632602213+3*1.12682503013197/1.885649142323237+3*1.13809328043329/1.979931599439399+3*1.149474213237623/2.078928179411369
=1.863738+3*1.12682503013197/1.885649142323237+3*1.13809328043329/1.979931599439399+3*1.149474213237623/2.078928179411369
=1.863738+3.380475/1.885649142323237+3*1.13809328043329/1.979931599439399+3*1.149474213237623/2.078928179411369
=1.863738+1.792738+3*1.13809328043329/1.979931599439399+3*1.149474213237623/2.078928179411369
=1.863738+1.792738+3.41428/1.979931599439399+3*1.149474213237623/2.078928179411369
=1.863738+1.792738+1.724443+3*1.149474213237623/2.078928179411369
=1.863738+1.792738+1.724443+3.448423/2.078928179411369
=1.863738+1.792738+1.724443+1.65875
=3.656476+1.724443+1.65875
=5.380919+1.65875
=7.039669
Answer:3*(1+1%)^11/(1+5%)^12+3*(1+1%)^12/(1+5%)^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15=7.039669
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation 3*(1+1%)^11/(1+5%)^12+3*(1+1%)^12/(1+5%)^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15 .
Question type: Mathematical calculation
Solution:
3*(1+1%)^11/(1+5%)^12+3*(1+1%)^12/(1+5%)^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/(1+5%)^12+3*(1+1%)^12/(1+5%)^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/1.05^12+3*(1+1%)^12/(1+5%)^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/1.05^12+3*1.01^12/(1+5%)^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/1.05^12+3*1.01^12/1.05^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/1.05^12+3*1.01^12/1.05^13+3*1.01^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/1.05^12+3*1.01^12/1.05^13+3*1.01^13/1.05^14+3*(1+1%)^14/(1+5%)^15
=3*1.01^11/1.05^12+3*1.01^12/1.05^13+3*1.01^13/1.05^14+3*1.01^14/(1+5%)^15
=3*1.01^11/1.05^12+3*1.01^12/1.05^13+3*1.01^13/1.05^14+3*1.01^14/1.05^15
=3*1.115668346665317/1.05^12+3*1.01^12/1.05^13+3*1.01^13/1.05^14+3*1.01^14/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.01^12/1.05^13+3*1.01^13/1.05^14+3*1.01^14/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.12682503013197/1.05^13+3*1.01^13/1.05^14+3*1.01^14/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.12682503013197/1.885649142323237+3*1.01^13/1.05^14+3*1.01^14/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.12682503013197/1.885649142323237+3*1.13809328043329/1.05^14+3*1.01^14/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.12682503013197/1.885649142323237+3*1.13809328043329/1.979931599439399+3*1.01^14/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.12682503013197/1.885649142323237+3*1.13809328043329/1.979931599439399+3*1.149474213237623/1.05^15
=3*1.115668346665317/1.79585632602213+3*1.12682503013197/1.885649142323237+3*1.13809328043329/1.979931599439399+3*1.149474213237623/2.078928179411369
=3.347005/1.79585632602213+3*1.12682503013197/1.885649142323237+3*1.13809328043329/1.979931599439399+3*1.149474213237623/2.078928179411369
=1.863738+3*1.12682503013197/1.885649142323237+3*1.13809328043329/1.979931599439399+3*1.149474213237623/2.078928179411369
=1.863738+3.380475/1.885649142323237+3*1.13809328043329/1.979931599439399+3*1.149474213237623/2.078928179411369
=1.863738+1.792738+3*1.13809328043329/1.979931599439399+3*1.149474213237623/2.078928179411369
=1.863738+1.792738+3.41428/1.979931599439399+3*1.149474213237623/2.078928179411369
=1.863738+1.792738+1.724443+3*1.149474213237623/2.078928179411369
=1.863738+1.792738+1.724443+3.448423/2.078928179411369
=1.863738+1.792738+1.724443+1.65875
=3.656476+1.724443+1.65875
=5.380919+1.65875
=7.039669
Answer:3*(1+1%)^11/(1+5%)^12+3*(1+1%)^12/(1+5%)^13+3*(1+1%)^13/(1+5%)^14+3*(1+1%)^14/(1+5%)^15=7.039669