# Sequences.

• Feb 24th 2011, 05:55 AM
ashishgaurav
Sequences.
The sum of n terms of the sequence 1,8,27,64,125,216.... is ________? Please, provide the explanation as well on how you arrived on the result. I know the answer is {n^2x(n+1)^2}/4 but, I simply can't figure out how it came. Any help will be appreciated. If anyone finds a different answer and can prove it, even it will work. I just want to know HOW IT CAME.
Thanks to all.
• Feb 24th 2011, 06:04 AM
Plato
Quote:

Originally Posted by ashishgaurav
The sum of n terms of the sequence 1,8,27,64,125,216.... is ________?

That sequence is just $\displaystyle a_n=n^3$.
So find $\displaystyle \sum\limits_{k = 1}^n {k^3 }.$
• Feb 24th 2011, 05:23 PM
skeeter
look at the sequence of partial sums ...

$\displaystyle 1 , 9 , 36 , 100 , 225 , ...$

$\displaystyle 1^2 , 3^2 , 6^2 , 10^2 , 15^2 , ...$

note that the sequence $\displaystyle 1 , 3 , 6 , 10 , 15 , ...$ is the sequence of triangular numbers whose nth term is

$\displaystyle \dfrac{n(n+1)}{2}$
• Feb 24th 2011, 07:36 PM
Wilmer