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1/1^4+1/2^4+1/3^4.........=pie^4/90 then 1/1^4+1/3^4................... is

1/1^4+1/2^4+1/3^4.........=pie^4/90 then 1/1^4+1/3^4................... is

Grade:10

1 Answers

Arun
25750 Points
6 years ago
Dear Nimish
 
1/1^4+1/2^4+1/3^4......=pie^4/90= (1/1^4+1/3^4+1/5^4 .....)+(1/2^4+1/4^4+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(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 RegardsArun (askIITians forum expert)

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