# Is this expression true?

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?

## migrated from mathoverflow.netJan 11 at 14:41

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• This is false if $b_1=\cdots =b_n=1$ and $\alpha >2$. – abx Jan 5 at 5:21
• You are asking in the wrong forum, I think. – GEdgar Jan 5 at 14:03
• There is a problem when $b_1 = h$, $b_2 = -h$, and $\alpha = -1$. I think you're missing some constraints if you want this to be true. – Eric Towers Jan 11 at 15:00