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 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 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

For which positive integers n is the ratio (sum_(k=1)^(n)k^(2))/(sum_(k=1)^(n)k) an integer?

The value of n for which the equation x^(n)+x^(-n)=k will be a quadratic equation is 1.

For which positive integers n is the ratio, (sum+(k=1)^(n) k^(2))/(sum_(k=1)^(n) k) an integer ?

The roots alpha and beta of the quadratic equation x^(2) - 5x + 3(k-1) = 0 are such that alpha- beta=1. Find the value k

If, for a positive integer n, the quadratic equation, x(x + 1) + (x + 1)(x + 2) +.....+ (x +bar( n-1))(x + n) = 10n has two consecutive integral solutions, then n is equal to

If,for a positive integer n,the quadratic equation,x(x+1)+(x+1)(x+2)+......+(x+bar(n)-1)(x+n)=10n has two consecutive integral solutions,then n is equal to