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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 .....
 

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1 Answers

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





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