Lt(1+a+a^(2)+......+a^(n-1))/(n rarr oo)(1+a+b)/(1+b+b^(2)+......+b^(n-1))=0" then "

underset(n to oo)lim (1+a+a^(2)+.....+a^(n-1))/(1+b+b^(2)+...+b^(n-1))=0 if

Lt_(n rarr oo)(1+(1)/(n))^(n)

Lt_(n rarr oo)(1+(1)/(n))^(n)

Lt_(n rarr oo)(1.3.5...(2n-1))/(2.4.6...(2n))=

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

lim_(n rarr oo)(a^(n)+b^(n))/(a^(n)-b^(n)), where a

lim_ (n rarr oo) ((a-1 + b ^ ((1) / (n))) / (a)) ^ (n)

{:(" "Lt),(n rarr oo):}{ (1)/(2n+1)+(1)/(2n+2)+......+(1)/(3n)}=

Let a = lim_(n rarr oo) (1+2+3+.....+n)/(n^(2))= , b = lim_(n rarr oo) (1^(2)+2^(2)+.....+n^(2))/(n^(3))= then

Lt_(n rarr oo)[(1)/(3n+1) + (1)/(3n+2)+…+(1)/(4n)]