Find `lim_(n->oo) [ 1/(n+1) +1/(n+2) +......+1/(n+5n)]`

lim_(n->oo) nsin(1/n)

Evaluate: lim_(n->oo)[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

Evalute lim_(n->oo)[1/((n+1)(n+2))+1/((n+2)(n+4))+......+1/(6n^2)]

If the value of lim_(n->oo){1/(n+1)+1/(n+2)+.......+1/(6n)} is 'K' then find value of (K - log_e 6)? .

lim_(n->oo)2^(n-1)sin(a/2^n)

Evaluate lim_(n->oo)n[1/((n+1)(n+2))+1/((n+2)(n+4))+....+1/(6n^2)]

lim_(n rarr oo)2^(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

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

The value of lim_(n->oo) n^(1/n)