`lim_(n->oo)nsum_(k=0)^(n-1)sum_(k=0)^(n-1)int_(k / n)^((k+1)/n)sqrt((x-k/n)((k+1)/n-x))dx` is `pi/k` then `k`

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

Evaluate: lim_ (n rarr oo) (1) / (n ^ (2)) sum_ (k = 0) ^ (n-1) [k int_ (k) ^ (k + 1) sqrt ((xk) (k + 1-x)) dx]

lim_ (n rarr oo) sum_ (k = 0) ^ (n) ((1) / (nC_ (k)))

lim_(n rarr oo) 1/n^(3) sum_(k=1)^(n) k^(2)x =

lim_ (n rarr oo) sum_ (k = 1) ^ (n) (k ^ (2)) / (2 ^ (k))

Find the sum_(k=1)^(oo) sum_(n=1)^(oo)k/(2^(n+k)) .

Find the sum_(k=1)^(oo) sum_(n=1)^(oo)k/(2^(n+k)) .

Find the sum_(k=1)^(oo) sum_(n=1)^(oo)k/(2^(n+k)) .