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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

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
6 years ago
Hello student, Please find the solution

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*\frac{1}{(1+1/2^4)}

Now you can simplyfy

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