If the sum of the series `sum_(m=1)^oo sum_(n-1)^oo (m^2n)/(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

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

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

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

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

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

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

COnsider the sequence (a_(n))n>=1, such that sum_(k=1)^(n)a_(k)=(3n^(2)+9n)/(2)AA n>=1. If lim_(n rarr oo)(1)/(na_(n))sum_(k=1)^(n)a_(k)=(p)/(q) (where p and q are coprime),then (p+q) is equal to

If lim_(n rarr oo)sum_(k=1)^(n)(k^(2)+k)/(n^(3)+k) can be expressed as rational (p)/(q) in the lowest form then the value of (p+q), is