# Powers

• February 29th 2012, 01:51 PM
spruancejr
Powers
I have $(1+2+...+n)^2 + (n+1)^3$

How do I go about transforming it into $(1+2+...+n+(n+1))^2$?
• February 29th 2012, 02:54 PM
Plato
Re: Powers
Quote:

Originally Posted by spruancejr
I have $(1+2+...+n)^2 + (n+1)^3$
How do I go about transforming it into $(1+2+...+n+(n+1))^2$?

Hints:
$(1 + 2 + \cdots + n)^2 + (n + 1)^3 = \left[ {\frac{{n(n + 1)}}{2}} \right]^2 + (n + 1)^3$
&
$(1 + 2 + \cdots + n+(n+1))^2 = \left[ {\frac{{(n+1)(n + 2)}}{2}} \right]^2$
• March 1st 2012, 10:48 AM
spruancejr
Re: Powers
Thanks! It's so simple and beautiful now...