hey everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I recently bought the the Dover Series book on Number Theory, and the 2nd example on page 5 asks your to prove

[tex]1^3 + 2^3 + 3^3 ... + n^3 = (1 + 2 + 3....)^2 [/tex]

Now, we've already proved that [tex]S_n = \frac{n(n+1)}{2}[/tex]

So here's how I proved it...

[tex]

(S_n)^2 = (\frac{n(n+1)}{2})^2 [/tex]

before we proved how [tex] S_k+1 = S_k + (k + 1) [/tex]

Which lead me to...

[tex] \frac{1}(k+1)^2((k+1)+1)^2{4} + (k+1)^2 [/tex]

[tex] = \sqrt{\frac{(k+1)^2((k+1)+1)^2}{4} + (k+1)^2} [/tex]

[tex] = \frac{(k+1)((k+1)+1)}{2} + (k+1) [/tex]

therefor...

[tex] S_k+1 = Sk + (k+1) [/tex]

Now I'm worried that I didnt really solve anything. I'm totally knew at this, and I'm open to criticism and help, just be kind :)

(ps.. this is my first time posting formulas, hopefully I did it right)

Thanks

dleacock

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# First attempt at a proof

**Physics Forums | Science Articles, Homework Help, Discussion**