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**spruancejr** · February 29th 2012, 01:51 PM

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

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

**Plato** · February 29th 2012, 02:54 PM

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

**spruancejr** · March 1st 2012, 10:48 AM

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

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