Find `lim_(n->oo) (1/2+1/4+1/8+....+1/2^n)`

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

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

lim_(n->oo) {1/1.3+1/3.5+1/5.7+.....+1/((2n+1)(2n+3)) is equal to

lim_(n->oo) (1.2+2.3+3.4+....+n(n+1))/n^3

f'(0) = lim_(n->oo) nf(1/n) and f(0)=0 Using this, find lim_(n->oo)((n+1)(2/pi)cos^(- 1)(1/n)-n)),|cos^(-1)1/n|

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)? .

Find the value of lim_(n->oo) (1+2+3+.......+n)/n^2

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

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

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