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

For any integer n>=1, then sum_(k=1)^(n)k(k+2)=

Find the value of sum_(i=1)^n sum_(i=1)^n sum_(k=1)^n k

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

If n is a positive integer SC_(k)=^(n)C_(k), find the value of (sum_(k=1)^(n)(k^(3))/(n(n+1)^(2)*(n+2))((C_(k))/(C_(k)-1))^(2))^(-1)

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 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