a question on series

If 11⁴+12⁴+13⁴+.......âˆž is Ï€⁴90, then 11⁴+13⁴+15⁴+.......âˆž=

a)Ï€⁴96
b)Ï€⁴100
c)Ï€⁴121
d)Ï€⁴108

Plz show the steps also as I dont even know how to start this prob...
here,Ï€ is pi.

2 Answers

Î£ 1n⁴ = Ï€⁴ 90.......(1)

divide both sides by 2⁴

so Î£ 1(2n)⁴= Ï€⁴ (90)16...(2)

subtract eqn 2 frm 1

11⁴+13⁴+15⁴+... = Ï€⁴90(1-1/16)= 15Ï€⁴(90)(16)

=Ï€⁴96

Thank you for the quick reply.

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