Let the sum sum_(n=1)^(9)1/(n(n+1)(n+2)) written in the rational form be p/q (where p and q are ...

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

Q.sum_(n=1)^(13)(i^(n)+i^(n+1))=(-1+i),n in N

Let a_(n)=sum_(k=1)^(n)(1)/(k(n+1-k)), then for n>=2

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).

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

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

Let S_(k), be defined as sum_(n=1)^(oo)((1)/(k))^(n) where k is positive integer greater than one.If the maximum value of expression (s_(k)*s_(k+2))/((s_(k+1))^(2))can be expressed in the lowest rational as (p)/(q). find the value of (p+q)