- #1

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## Homework Statement

Let [itex] g(x) = \frac{x}{e^x - 1} = \sum_{n=0}^{\infty} \frac{B_n}{n!} x^n[/itex] be the taylor series for g about 0. Show B_0 = 1 and [itex] \sum_{k=0}^{n} \binom{n+1}{k} B_k = 0 [/itex].

## Homework Equations

## The Attempt at a Solution

[itex] g(x) = \sum_{n=0}^{\infty} \frac{g^{(n)}(0)}{n!} x^n [/itex], but [itex] g^{(n)}(0) [/itex] is always undefined at 0. So I don't see how any of these relations can hold.