The constant term of the quadratic expression `sum_(k=2)^n(x-1/(k-1))(x-1/k)`, as `n->oo` is

The constant term of the quadratic expression sum_(k=2)^(n)(x-(1)/(k-1))(x-(1)/(k)), as n rarr oo is

The value of the positve integer n for which the quadratic equation sum_(k=1)^(n)(x+k-1)(x+k)=10n has solutions alpha and alpha+1 for some alpha is

sum_(k =1)^(n) k(1 + 1/n)^(k -1) =

The number of real roots of equation sum_(k=1)^(oo)(x-k^(k))^(7)=0;(n>5)

Evaluate : sum_(k=1)^n (2^k+3^(k-1))

Interval of convergence of the power series sum_(k=1)^(oo)((x+2)^(k))/(k sqrt(k+1)) is

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

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)

Evaluate the limit: lim_(x rarr1)(sum_(k=1)^(oo0)x^(k)-100)/(x-1)