Finite sum inequality (math GRE subject)

Question

Which of the following statements are true:

1. There exists a constants $C$ such that $\log x \leq C\sqrt x$ for all $x\geq1$
2. There exists a constant $C$ such that $\sum_{k=1}^nk^2 \leq Cn^2$ for all integers $n\geq1$
3. There exists a constant $C$ such that $|\sin x-x|\leq C|x^3|$

So the correct answer is 1 and 3. Why is 2 false? It seems to me that you could find some constant C whose product with $n$ is greater than an entire sum of $k^2$ up to $n$

Answer 1

Sum of squares $\sum_{k=1}^nk^2=\frac{n(n+1)(n+2)}{6}$

so, it is proportional to $n^3$.