For the natural numbers `n, k , let T(n,k) = 1/((n+1)!)+1/((n+2)!)+1/((n+3)!)+......1/((n+k)!)` then which of the following is false

Evaluate lim_(nrarroo) [1/(n+k) + 1/(n+2k) + 1/(n+3k) +…+ 1/(n+nk)]

Compute ((1+k)(1+k/2) ..... (1+k/n))/((1+n)(1+n/2) ..... (1+n/k))

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

If sum_(n=1)^(5)(1)/(n(n+1)(n+2)(n+3))=(k)/(3), then k is equal to :-

Let f(n)=(sum_(r=1)^(n)((1)/(r)))/(sum_(k=1)^(n)(k)/(2n-2k+1)(2n-k+1))

If .^(n)C_(3)=k.n(n-1)(n-2) then k=

Let z_(1)z_(2),z_(3)...z_(n) be the complex numbers such that |z_(1)|=|z_(2)|...|z_(n)|=1. If z=(sum_(k=1)^(n)z_(k))(sum_(k=1)^(n)(1)/(z_(k))) then proves that z is a real number 0

If n in N and sum_(k=1)^(n)k^(3)((C_(k))/(C_(k-1)))^(2)=(n(n+1)^(2)(n+2))/(3p) then the value of p is