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

The value of sum_(n=1)^(oo)(1)/((3n-2)(3n+1)) is equal to (p)/(q), where p and q are relatively prime natural numbers.Then the value of (p^(2)+q^(2)) is equal to

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

The value of sum_(n=1)^(oo)(4n-2)/(3^(n))

sum_ (n = 1) ^ (oo) (1) / ((n + 1) (n + 2) (n + 3) ........ (n + k))

The sum sum_(n=1)^(oo)tan^(-1)((3)/(n^(2)+n-1)) is equal to

sum_ (n = 0)^(oo) ((2i)/(3))^(n) =

The value of the sum_(n=0)^(oo)(2n+3)/(3^(n)) is equal to

Let (:a_(n):) be a sequence given by a_(n+1)=3a_(n)-2*a_(n-1) and a_(0)=2,a_(1)=3 then the value of sum_(n=1)^(oo)(1)/(a_(n)-1) equals (A) 1 (B) (1)/(2) (C) 2 D) 4