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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%)^41+3/(1+5%)^42+3/(1+5%)^43+3/(1+5%)^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50 .
Question type: Mathematical calculation
Solution:
3/(1+5%)^41+3/(1+5%)^42+3/(1+5%)^43+3/(1+5%)^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/(1+5%)^42+3/(1+5%)^43+3/(1+5%)^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/(1+5%)^43+3/(1+5%)^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/(1+5%)^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+0.33389+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+0.33389+0.31799+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+0.33389+0.31799+0.302848+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+0.33389+0.31799+0.302848+0.288426+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+0.33389+0.31799+0.302848+0.288426+0.274692+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+0.33389+0.31799+0.302848+0.288426+0.274692+0.261611
=0.792364+0.368113+0.350584+0.33389+0.31799+0.302848+0.288426+0.274692+0.261611
=1.160477+0.350584+0.33389+0.31799+0.302848+0.288426+0.274692+0.261611
=1.511061+0.33389+0.31799+0.302848+0.288426+0.274692+0.261611
=1.844951+0.31799+0.302848+0.288426+0.274692+0.261611
=2.162941+0.302848+0.288426+0.274692+0.261611
=2.465789+0.288426+0.274692+0.261611
=2.754215+0.274692+0.261611
=3.028907+0.261611
=3.290518
Answer:3/(1+5%)^41+3/(1+5%)^42+3/(1+5%)^43+3/(1+5%)^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50=3.290518
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation 3/(1+5%)^41+3/(1+5%)^42+3/(1+5%)^43+3/(1+5%)^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50 .
Question type: Mathematical calculation
Solution:
3/(1+5%)^41+3/(1+5%)^42+3/(1+5%)^43+3/(1+5%)^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/(1+5%)^42+3/(1+5%)^43+3/(1+5%)^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/(1+5%)^43+3/(1+5%)^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/(1+5%)^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/(1+5%)^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/(1+5%)^50
=3/1.05^41+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/1.05^42+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/1.05^43+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/1.05^44+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/1.05^45+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/1.05^46+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/1.05^47+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/1.05^48+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/1.05^49+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/1.05^50
=3/7.391988147730891+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+3/7.761587555117436+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+3/8.149666932873309+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+3/8.557150279516975+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+3/8.985007793492823+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+0.33389+3/9.434258183167465+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+0.33389+0.31799+3/9.905971092325839+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+0.33389+0.31799+0.302848+3/10.401269646942131+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+0.33389+0.31799+0.302848+0.288426+3/10.921333129289238+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+0.33389+0.31799+0.302848+0.288426+0.274692+3/11.467399785753701
=0.405845+0.386519+0.368113+0.350584+0.33389+0.31799+0.302848+0.288426+0.274692+0.261611
=0.792364+0.368113+0.350584+0.33389+0.31799+0.302848+0.288426+0.274692+0.261611
=1.160477+0.350584+0.33389+0.31799+0.302848+0.288426+0.274692+0.261611
=1.511061+0.33389+0.31799+0.302848+0.288426+0.274692+0.261611
=1.844951+0.31799+0.302848+0.288426+0.274692+0.261611
=2.162941+0.302848+0.288426+0.274692+0.261611
=2.465789+0.288426+0.274692+0.261611
=2.754215+0.274692+0.261611
=3.028907+0.261611
=3.290518
Answer:3/(1+5%)^41+3/(1+5%)^42+3/(1+5%)^43+3/(1+5%)^44+3/(1+5%)^45+3/(1+5%)^46+3/(1+5%)^47+3/(1+5%)^48+3/(1+5%)^49+3/(1+5%)^50=3.290518