`underset(n→∞)lim1/n^(3){1+3+6+......+(n(n+1))/2}` =

lim_ (n rarr oo) (1) / (n ^ (3)) {1 + 3 + 6 + ...... + (n (n + 1)) / (2)}

Prove that underset( n rarr oo)lim x_(n)=1, if x_(n)=(3^(n)+1)/3^(n) .

Find underset( n rarr oo )("lim") ( ( 2 n^(3))/( 2n^(2) + 3)- ( 1+ 5n^(2) )/( 5n + 1))

underset(n to oo)lim ((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1))

Find underset(n to oo)lim ((2n^(3))/(2n^(2)+3)+(1-5n^(2))/(5n+1))

underset(n to oo)lim {1/(1-n^(2))+(2)/(1-n^(2))+....+(n)/(1-n^(2))} is equal to

lim_ (n rarr oo) {(1) / (n ^ (3) +1) + (4) / (n ^ (3) +1) + (9) / (n ^ (3) +1) +. ........... + (n ^ (2)) / (n ^ (3) +1)}