If the sum and product of four positive consecutive terms of a G.P., are $126$ and $1296$, respectively, then the sum of common ratios of all such GPs is

The sum to $10$terms of the series

$\frac{1}{1+1^2+1^4}+\frac{2}{1+2^2+2^4}+\frac{3}{1+3^2+3^4}+\dots$is :-

The sum $\sum _{n=1}^{\infty }\frac{2n^2+3n+4}{\left(2n\right)!}$  is equal to :

The sum of the common terms of the following three arithmetic progressions.

$3,7,11,15,\dots \dots \dots \dots ,399$

$2,5,8,11,.........359$  and

$2,7,12,17,\dots \dots ,197$, is equal to _____ .