Evaluate the limit (1^3+2^3+...+n^3)/n^4. n-->infinite.

Before starting the evaluation of the limit, we'll
re-write the sum of the numerator:

1^3+2^3+...+n^3 =
[n*(n+1)/2]^2

To evaluate the limit of the rational
function, when n tends to +inf.,we'll factorize both, numerator and
denominator.

We'll substitute the numerator, by the result
of the sum, we'll factorize  by the highest power of n, which in this case is
n^4.

We'll have:

lim
(1^3+2^3+...+n^3)/n^4 = lim n^2*(n+1)^2/4*lim n^4

lim
(1^3+2^3+...+n^3)/n^4 = lim n^4(1/n^2+2/n+1)/4*lim
n^4

We'll divide by
n^4:

lim (1/n^2+2/n+1)/4*lim 1 =
(0+0+1)/4*1

lim
(1^3+2^3+...+n^3)/n^4 = 1/4