[" 2.Find the value of the positive integer "n" for which the quadratic equation "],[qquad sum_(k=1)^(n)(x+k-1)(x+k)=10n]

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

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

Find sum_(k=1)^(n)(1)/(k(k+1)) .

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

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

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