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if 1/1^4+1/2^4+1/3^4......=pie^4/90then find answer for  1/1^4+1/3^4+1/5^4 .....

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3 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question below
[1/1^4+1/2^4+1/3^4 +1/4^4+1/5^4+1/6^4......=pi ^4/90]
[(1/1^4+1/3^4+1/5^4 + .....)+(1/2^4+1/4^4+1/6^4+......)=pi ^4/90]
[(1/1^4+1/3^4+1/5^4 + .....)+1/2^4 (1/1^4+1/2^4+1/3^4+......)=pi ^4/90]
[(1+1/2^4)(1/1^4+1/2^4+1/3^4+......)=pi ^4/90]
[(1/1^4+1/2^4+1/3^4+......)=pi ^4/90*{(1/(1+1/2^4)}]
so we get(1/1^4+1/2^4+1/3^4+......)=8pi ^4/765
Pustam Raut
11 Points
3 years ago
1/1⁴+1/2⁴+1/3⁴+1/4⁴+1/5⁴+1/6⁴+...=π⁴/90i.e.(1/1⁴+1/3⁴+1/5⁴+...)+(1/2⁴+1/4⁴+1/6⁴+...)=π⁴/90i.e.(1/1⁴+1/3⁴+1/5⁴+...)+(1/2⁴)*(1/1⁴+1/2⁴+1/3⁴+...)=π⁴/90i.e.(1/1⁴+1/3⁴+1/5⁴+...)+(1/16)×π⁴/90=π⁴/90i.e.1/1⁴+1/3⁴+1/5⁴+...=(1-1/16)×π⁴/90=15π⁴/(16×90)=π⁴/96Hence,1/1⁴+1/3⁴+1/5⁴+...=π⁴/96Similarly,1/1⁴-1/2⁴+1/3⁴-1/4⁴+1/5⁴-1/6⁴+...=7π⁴/720
Chaman Lal
13 Points
2 years ago
1/1^4+1/2^4+1/3^4+1/4^4........=π^4/90
1/1^4+1/3^4+1/5^4.....=π^4/90-(1/2^4+1/4^4+1/6^4)
" " " " =π^4/90-1/2^4(1/1^4+1/2^4+1/3^4+1/4^4.....)
" " " "=π^4/90-1/2^4(π^4/90)
Simplify and you will get the answer=π^4/96

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