`lim_(n->oo)(1^k+2^k+...+n^k)/(k*n^(k+1)),(n in NN , k in I^+)`

lim_ (n rarr oo) (1 ^ (k) + 2 ^ (k) + ... + n ^ (k)) / (k * n ^ (k + 1)), (n in N, k in I ^ (+))

k ne -1 is a constant. The value of lim_(n to oo)(1^k + 2^k + …. + n^k)/(k(n^(k+1))) is

lim_(n toinfty)[(1^(k) +2^(k)+3^(k) +. . .. +n^(k))/(n^(k +1))]=

Evaluate lim_(n rarr oo)(2^(k) + 4^(k) + 6^(k)+…+(2n)^(k))/(n^(k+1)) by using the method of finding definite integral as the limit of a sum.

lim_ (n rarr oo) sum_ (k = 1) ^ (n) (k) / (n ^ (2) + k ^ (2)) is equals to

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