Find`lim_(n->00)(1.2+2.3+3.4+4.5+........+n(n+1))/n^3`

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

lim_(n->oo)(1^2+2^2+3^2+..........+n^2)/n^3

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

The value of lim_(n->oo) (1^2 . n+2^2.(n-1)+......+n^2 . 1)/(1^3+2^3+......+n^3) is equal to

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

lim_(n -> oo) (((n+1)(n+2)(n+3).......2n) / n^(2n))^(1/n) is equal to

Let alpha=lim_(n->oo)((1^3-1^2)+(2^3-2^2)+.....+(n^3-n^2))/(n^4), then alpha is equal to :

The value of lim_(n to oo)((1)/(1^(3)+n^(3))+(2^(2))/(2^(3)+n^(3))+..........+(n^(2))/(n^(3)+n^(3))) is :

Prove the following by using the principle of mathematical induction for all n in N : 1. 2. 3 + 2. 3. 4 + .. . + n(n + 1) (n + 2)=(n(n+1)(n+2)(n+3))/4

The sum of the series 1+4+3+6+5+8+ upto n term when n is an even number (n^2+n)/4 2. (n^2+3n)/2 3. (n^2+1)/4 4. (n(n-1))/4 (n^2+3n)/4