Question

It is given that 1/1⁴ + 1/2⁴ + 1/3⁴ + ......∞ = π⁴/90 then, |+ 1/3⁴ + 1/5⁴ + ........ ∞

(a)  π⁴/96

(b)  π⁴/45

(c)   89π⁴/90

(d)  None of these

Answer 1

Correct option (a)  π⁴/96

Explanation:

Let   1/1⁴ + 1/3⁴ + 1/5⁴ + ....  ∞ = S

Now  1/1⁴ + 1/2⁴ + 1/3⁴ + ......∞  = π⁴/90

(1/1⁴ + 1/3⁴ + 1/5⁴ + ....) + (1/2⁴ + 1/4⁴ + 1/6⁴ + ...) = π⁴/90

⇒ S + 1/2⁴ (1/1⁴ + 1/2⁴ + 1/3⁴ + ........ ∞)  = π⁴/90

⇒ S + 1/16 .π⁴/90 = π⁴/90

⇒ S = π⁴/90(1 - 1/16) = π⁴/90 x 15/90 = π⁴/96