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

The value of the positive 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

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

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

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

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)

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