Evaluate `sum_(m=1)^(oo)sum_(n=1)^(oo)(m^(2)n)/(3^(m)(n*3^(m)+m*3^(n)))`.

If the sum of the series sum_(m=1)^(oo)sum_(n-1)^(oo)(m^(2)n)/(3^(m)(n.3^(m)+m.3^(n))) can be expressed as (p)/(q) where p and q are co-prime number, then (q-3p) is equal to

Find the sum sum_(n=1)^(oo)(6^(n))/((3^(n)-2^(n))(3^(n+1)-2^(n+1)))

Find the sum sum_(n=1)^(oo)(6^(n))/((3^(n)-2^(n))(3^(n+1)-2^(n+1)))

The value of sum_(n=1)^(10) sum_(m=1)^(10) (m^(2)+n^(2)) equals

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

Find the value of S_(n)=sum_(n=1)^(oo)(3^(n)*5^(n))/((5^(n)-3^(n))(5^(n-1)-3^(n+1))) and hence s_(oo)

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