# Summation

• August 19th 2009, 06:43 AM
BooGTS
Summation
This would be alot easier if I could do the html markup for it, but here goes:

lim as n ==> oo

n is above the epsilon, k=1 below of:

(1-(k/n))^3 (2/n)

Evaluate

For a summation involving i^3, the summation formula is (n^2(n+1)^2)/4 but thats as far as I can get as far as where to start. Help? and thanks!
• August 19th 2009, 07:27 AM
red_dog
$\lim_{n\to\infty}\sum_{k=1}^n\left(1-\frac{k}{n}\right)^3\cdot\frac{2}{n}=2\lim_{n\to\i nfty}\frac{1}{n}\sum_{k=1}^n\left(1-\frac{k}{n}\right)^3=2\int_0^1(1-x)^3dx$