- #1

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- 7

- Homework Statement
- How do I show that ##1+2^{2} + 3^{3} +...+n^{2} > \frac {1}{3} \cdot n^{3}## ?

- Relevant Equations
- k

My first attempt was ##... + n^{2} + (n+1)^{2} > \frac {1}{3} n^{3} + (n+1)^{2}##

then we must show that ##\frac {1}{3} n^{3} + (n+1)^{2} > \frac {1}{3} (n+1)^{3}##

We evaluate both sides and see that the LHS is indeed bigger than RHS. However, this solution is inconsistent so I am asking for some guidance as to a better method...

then we must show that ##\frac {1}{3} n^{3} + (n+1)^{2} > \frac {1}{3} (n+1)^{3}##

We evaluate both sides and see that the LHS is indeed bigger than RHS. However, this solution is inconsistent so I am asking for some guidance as to a better method...