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

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

Grade:

1 Answers

Sunil Raikwar
askIITians Faculty 45 Points
6 years ago
1/1^4+1/2^4+1/3^4+1/4^4+1/5^4......=pie^4/90
(1/1^4+1/3^4+1/5^4 ....)+(1/2^4+1/4^4+1/6^4.................=pie^4/90
(1/1^4+1/3^4+1/5^4 ....)+1/2^4(1/1^4+1/2^4+1/3^4.................=pie^4/90
(1/1^4+1/3^4+1/5^4 ....)+1/16.pie^4/90=pie^4/90
(1/1^4+1/3^4+1/5^4 ....)=pie^4/90(1-1/16)=pie^4/90(15/16)=pie^4/96



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