Is this expression true?

Question

Let $a_1=b_1/h,...,a_n=b_n/h\in\mathbb{R}$ with $h\in\mathbb{R}$ small. It's true that, given a $\alpha\in\mathbb{R}$: \begin{eqnarray} (a_1+...+a_n)^\alpha=\sum_{i=1}^n (a_i)^\alpha+\mathcal{O}\left(\frac{1}{h^2}\right) \end{eqnarray} ?? Is there any (good) reference where there is proof of some theorem / lemma that I can use to justify this?