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

If sum _( k =1) ^(oo) (k^(2))/(3 ^(k))=p/q, where p and q are relatively prime positive integers. Find the value of (p-q),

If sum _( k =1) ^(oo) (k^(2))/(3 ^(k))=p/q, where p and q are relatively prime positive integers. Find the value of (p+q),

If sum _( k =1) ^(oo) (k^(2))/(3 ^(k))=p/q, where p and q are relatively prime positive integers. Find the value of (p+q),

The sum sum_(n=1)^oo (n/(n^4+4)) is equal to p/q then q-p is ____

The sum sum_(n=1)^oo (n/(n^4+4)) is equal to p/q then q-p is ____

Let d bet the minimum value of f(x)=5x^(2)-2x+(26)/(5) and f(x) is symmetric about x=r. If sum_(n=1)^(n=1)(1+(n-1)d)r^(n-1) equals,(p)/(q), where p and q are relative prime,then find the value of (3q-p).

If the value of lim_(x->0)( ((3/ x)+1)/((3/x)-1))^(1/x) can be expressed in the form of e^(p/q), where p and q are relative prime then find the value of (p+q) .