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 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

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

The sum S_(n)=sum_(k=0)^(n)(-1)^(k)*^(3n)C_(k) , where n=1,2,…. is

The value of lim_(n->oo) sum_(k=1)^n log(1+k/n)^(1/n) ,is

If the sum of the zeros of the quadratic polynomial f(x)=k x^2-3x+5 is 1, write the value of k .

If |a| lt 1, b = sum_(k=1)^(oo) (a^(k))/(k) rArr a=

The value of integral sum _(k=1)^(n) int _(0)^(1) f(k - 1+x) dx is

The value of lim _( n to oo) sum _(k =1) ^(n) ((k)/(n ^(2) +n +2k))=

Prove that sum_(k=0)^(n) (-1)^(k).""^(3n)C_(k) = (-1)^(n). ""^(3n-1)C_(n)

The value of \lim_{n \to \infty } sum_(k=1)^n (n-k)/(n^2) cos((4k)/n) equals to