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If 1/1^4+1/2^4+1/3^4+...+oo=pi^4/90, the...

If `1/1^4+1/2^4+1/3^4+...+oo=pi^4/90,` then `1/1^4+1/3^4+1/5^4+...+oo=`

A

` (pi^(4))/(96)`

B

` (pi^(4))/45`

C

` (89)/(90)pi`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
a
Since , ` 1/(1^(2))+1/2^(4)+1/3^(4)+...= (pi^(4))/90`
` rArr (pi^(4))/90 = (1/1^(4)+1/3^(3)+...)+(1/(2^(4))+1/(4^(4))+1/(6^(4))+...)`
` rArr (pi^(4))/90 = (1/(1^(4))+1/(3^(4))+...)+1/(2^(4))(1/(1^(4))+1/(2^(4))+1/3^(4)+...)`
` rArr (pi^(4))/90 = (1/1^(4)+1/(3^(4))+...)+1/16((pi^(4))/90) rArr (pi^(4))/(90) rArr 1/(1^(4))+1/(3^(4))+...`
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