`lim_(n->oo)n^(- n^2)((n+1)(n+1/2)(n+1/2^2)....(n+1/(2^(n-1))))^n`

lim_ (n rarr oo) n ^ (- n ^ (2)) ((n + 1) (n + (1) / (2)) (n + (1) / (2 ^ (2))) .... (n + (1) / (2 ^ (n-1)))) ^ (n)

lim_(n rarr oo)[(1)/(n)+(1)/(n+1)+(1)/(n+2)+.....+(1)/(2n)]

lim_(n rarr oo)(2^(n)+3^(n))^(1/n)

Evaluate the following (i) lim_(n to oo)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))....+(n-1)/(n^(2))) (ii) lim_(n to oo)((1)/(n+1)+(1)/(n+2)+....+(1)/(2n)) (iii) lim_(n to oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+(n)/(2n^(2))) (iv) lim_(n to oo)((1^(p)+2^(p)+.....+n^(p)))/(n^(p+1)),pgt0

lim_(n->oo) (1)/(n^(6)){(n+1)^(5)+(n+2)^(5)+...+(2n)^(5)}

lim_(n -> oo) (((n+1)(n+2)(n+3).......3n) / n^(2n))^(1/n)is equal to

lim_(n rarr oo)[(1)/(n^(2))+(2)/(n^(2))+....+(n)/(n^(2))]

Evaluate: lim_(n rarr oo)[(1)/((n+1)^(2))+(1)/((n+2)^(2))+...+(1)/((2n)^(2))]

lim_ (n rarr oo) (2 ^ (n) -1) / (2 ^ (n) +1)