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=`

It is given that (1)/( 1^(4) ) + ( 1)/( 2^(4)) + ( 1)/( 3^(4)) +"......" to oo = ( pi^(4))/( 90) , then (1)/( 1^(4)) +( 1)/( 3^(4)) +( 1)/( 5^(4)) + "......" to oo is :

1/(2!)-1/(3!)+1/(4!) .....oo =

1+ 1/(2!)+2/(3!)+4/(4!)+ .... oo =

4+1/((5+1/(4+(1/(5+ . . . oo)))))=

(1/(1!) +1/(2!) +1/(3!) + .....oo) (1/(2!) -1/(3!) +1/(4!)-1/(5!) .....oo)

Prove that (1-1/3+1/3^(2)-1/3^(3)+1/3^(4)-...oo)=3/4

If | (1,4), (1., 3) |+| (1/2,4), (1/3,3) |+| (1/4,4), (1/9,3) |+.... oo = (i) 1 (ii) -1 (iii) 0 (iv) infty