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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%)^41+3*(1+1%)^12/(1+5%)^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45 .
Question type: Mathematical calculation
Solution:
3*(1+1%)^11/(1+5%)^41+3*(1+1%)^12/(1+5%)^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/(1+5%)^41+3*(1+1%)^12/(1+5%)^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*(1+1%)^12/(1+5%)^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/(1+5%)^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*1.01^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*1.01^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*1.01^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/1.05^41+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/1.05^42+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/1.05^43+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=3.347005/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+3.380475/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+0.435539+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+0.435539+3.41428/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+0.435539+0.418947+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+0.435539+0.418947+3.448423/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+0.435539+0.418947+0.402987+3*1.160968955369999/8.985007793492823
=0.452788+0.435539+0.418947+0.402987+3.482907/8.985007793492823
=0.452788+0.435539+0.418947+0.402987+0.387635
=0.888327+0.418947+0.402987+0.387635
=1.307274+0.402987+0.387635
=1.710261+0.387635
=2.097896
Answer:3*(1+1%)^11/(1+5%)^41+3*(1+1%)^12/(1+5%)^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45=2.097896
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation 3*(1+1%)^11/(1+5%)^41+3*(1+1%)^12/(1+5%)^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45 .
Question type: Mathematical calculation
Solution:
3*(1+1%)^11/(1+5%)^41+3*(1+1%)^12/(1+5%)^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/(1+5%)^41+3*(1+1%)^12/(1+5%)^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*(1+1%)^12/(1+5%)^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/(1+5%)^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*1.01^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*1.01^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*(1+1%)^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*1.01^15/(1+5%)^45
=3*1.01^11/1.05^41+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/1.05^41+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.01^12/1.05^42+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/1.05^42+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.01^13/1.05^43+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/1.05^43+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.01^14/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/1.05^44+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.01^15/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/1.05^45
=3*1.115668346665317/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=3.347005/7.391988147730891+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+3*1.12682503013197/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+3.380475/7.761587555117436+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+0.435539+3*1.13809328043329/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+0.435539+3.41428/8.149666932873309+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+0.435539+0.418947+3*1.149474213237623/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+0.435539+0.418947+3.448423/8.557150279516975+3*1.160968955369999/8.985007793492823
=0.452788+0.435539+0.418947+0.402987+3*1.160968955369999/8.985007793492823
=0.452788+0.435539+0.418947+0.402987+3.482907/8.985007793492823
=0.452788+0.435539+0.418947+0.402987+0.387635
=0.888327+0.418947+0.402987+0.387635
=1.307274+0.402987+0.387635
=1.710261+0.387635
=2.097896
Answer:3*(1+1%)^11/(1+5%)^41+3*(1+1%)^12/(1+5%)^42+3*(1+1%)^13/(1+5%)^43+3*(1+1%)^14/(1+5%)^44+3*(1+1%)^15/(1+5%)^45=2.097896