If `S=sum_(n=2)^oo (3n^2+1)/(n^2-1)^3` then `9/S=`

If S=sum_(n=2)^(oo)(3n^(2)+1)/((n^(2)-1)^(3)) then (9)/(4S) is

If S=sum_(n=1)^(10)(2n+(1)/(2)), then S

If S=sum_(n=0)^(oo)((log x)^(2n))/((2n)!) then S equals :

sum_(0)^(oo)(1)/((3n+1)(3n+2))

Let S_1 = 4+6/3+8/3^2+10/3^3+...+oo and S_2 =sum_(n=1)^oo 1/((3n+1)(3n+4)), then the value of the S_1/(10 S_2) is

Find the sum Sigma_(r=1)^(oo)(3n^2+1)/((n^2-1)^3)

If S_(n) = sum_(n=1)^(n) (2n + 1)/(n^(4) + 2n^(3) + n^(2)) then S_(10) is less then