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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 5/(1+5%)^41+5/(1+5%)^42+5/(1+5%)^43+5/(1+5%)^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49 .
Question type: Mathematical calculation
Solution:
5/(1+5%)^41+5/(1+5%)^42+5/(1+5%)^43+5/(1+5%)^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/(1+5%)^42+5/(1+5%)^43+5/(1+5%)^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/(1+5%)^43+5/(1+5%)^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/(1+5%)^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/1.05^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/1.05^44+5/1.05^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/1.05^44+5/1.05^45+5/1.05^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/1.05^44+5/1.05^45+5/1.05^46+5/1.05^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/1.05^44+5/1.05^45+5/1.05^46+5/1.05^47+5/1.05^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/1.05^44+5/1.05^45+5/1.05^46+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/1.05^42+5/1.05^43+5/1.05^44+5/1.05^45+5/1.05^46+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/1.05^43+5/1.05^44+5/1.05^45+5/1.05^46+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/1.05^44+5/1.05^45+5/1.05^46+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/1.05^45+5/1.05^46+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/1.05^46+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+0.613522+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+0.613522+0.584307+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+0.613522+0.584307+0.556483+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+0.613522+0.584307+0.556483+0.529983+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+0.613522+0.584307+0.556483+0.529983+0.504746+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+0.613522+0.584307+0.556483+0.529983+0.504746+0.480711+5/10.921333129289238
=0.676408+0.644198+0.613522+0.584307+0.556483+0.529983+0.504746+0.480711+0.45782
=1.320606+0.613522+0.584307+0.556483+0.529983+0.504746+0.480711+0.45782
=1.934128+0.584307+0.556483+0.529983+0.504746+0.480711+0.45782
=2.518435+0.556483+0.529983+0.504746+0.480711+0.45782
=3.074918+0.529983+0.504746+0.480711+0.45782
=3.604901+0.504746+0.480711+0.45782
=4.109647+0.480711+0.45782
=4.590358+0.45782
=5.048178
Answer:5/(1+5%)^41+5/(1+5%)^42+5/(1+5%)^43+5/(1+5%)^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49=5.048178
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation 5/(1+5%)^41+5/(1+5%)^42+5/(1+5%)^43+5/(1+5%)^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49 .
Question type: Mathematical calculation
Solution:
5/(1+5%)^41+5/(1+5%)^42+5/(1+5%)^43+5/(1+5%)^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/(1+5%)^42+5/(1+5%)^43+5/(1+5%)^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/(1+5%)^43+5/(1+5%)^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/(1+5%)^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/1.05^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/1.05^44+5/1.05^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/1.05^44+5/1.05^45+5/1.05^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/1.05^44+5/1.05^45+5/1.05^46+5/1.05^47+5/(1+5%)^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/1.05^44+5/1.05^45+5/1.05^46+5/1.05^47+5/1.05^48+5/(1+5%)^49
=5/1.05^41+5/1.05^42+5/1.05^43+5/1.05^44+5/1.05^45+5/1.05^46+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/1.05^42+5/1.05^43+5/1.05^44+5/1.05^45+5/1.05^46+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/1.05^43+5/1.05^44+5/1.05^45+5/1.05^46+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/1.05^44+5/1.05^45+5/1.05^46+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/1.05^45+5/1.05^46+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/1.05^46+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/1.05^47+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/1.05^48+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/1.05^49
=5/7.391988147730891+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+5/7.761587555117436+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+5/8.149666932873309+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+0.613522+5/8.557150279516975+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+0.613522+0.584307+5/8.985007793492823+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+0.613522+0.584307+0.556483+5/9.434258183167465+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+0.613522+0.584307+0.556483+0.529983+5/9.905971092325839+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+0.613522+0.584307+0.556483+0.529983+0.504746+5/10.401269646942131+5/10.921333129289238
=0.676408+0.644198+0.613522+0.584307+0.556483+0.529983+0.504746+0.480711+5/10.921333129289238
=0.676408+0.644198+0.613522+0.584307+0.556483+0.529983+0.504746+0.480711+0.45782
=1.320606+0.613522+0.584307+0.556483+0.529983+0.504746+0.480711+0.45782
=1.934128+0.584307+0.556483+0.529983+0.504746+0.480711+0.45782
=2.518435+0.556483+0.529983+0.504746+0.480711+0.45782
=3.074918+0.529983+0.504746+0.480711+0.45782
=3.604901+0.504746+0.480711+0.45782
=4.109647+0.480711+0.45782
=4.590358+0.45782
=5.048178
Answer:5/(1+5%)^41+5/(1+5%)^42+5/(1+5%)^43+5/(1+5%)^44+5/(1+5%)^45+5/(1+5%)^46+5/(1+5%)^47+5/(1+5%)^48+5/(1+5%)^49=5.048178