Math Help - Powers

1. Powers

I have $(1+2+...+n)^2 + (n+1)^3$

How do I go about transforming it into $(1+2+...+n+(n+1))^2$?

2. Re: Powers

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:
$(1 + 2 + \cdots + n)^2 + (n + 1)^3 = \left[ {\frac{{n(n + 1)}}{2}} \right]^2 + (n + 1)^3$
&
$(1 + 2 + \cdots + n+(n+1))^2 = \left[ {\frac{{(n+1)(n + 2)}}{2}} \right]^2$

3. Re: Powers

Thanks! It's so simple and beautiful now...