`log_(n->oo) (((1/2)^n-7)/(5+(1/2)^n))=.....`

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

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

Given that lim_(nto oo) sum_(r=1)^(n) (log (r+n)-log n)/(n)=2(log 2-(1)/(2)) , lim_(n to oo) (1)/(n^k)[(n+1)^k(n+2)^k.....(n+n)^k]^(1//n) , is

Given that lim_(nto oo) sum_(r=1)^(n) (log (r+n)-log n)/(n)=2(log 2-(1)/(2)) , lim_(n to oo) [(1)/(n^k)[(n+1)^k(n+2)^k.....(n+n)^k]]^(1//n) , is

lim_(n rarr oo)(1+(1)/(5)+(1)/(25)+.....+(1)/(5^(n)))/(1+(1)/(7)+(1)/(49)+.....+(1)/(7^(n))) =

lim_(n to oo)[(1+(1)/(5)+(1)/(25)+.....1/(5)^(n))/(1+(1)/(7)+(1)/(49)+....+(1)/(7^(n))]] =

If n=|__2002, evaluate (1)/(log_(2)n)+(1)/(log_(3)n)+(1)/(log_(4)n)+......+(1)/(log_(2002)n)

sum_(n=1)^(oo) ((log_ex)^(2n-1))/((2n-1)!)=

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)? .