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In the Euler–Maclaurin formula:

$$\sum_{n=a}^b \sim \int_a^b f(x)\;dx+\frac{f(a)+f(b)}{2}+\sum_{k=1}^\infty\frac{B_{2k}}{(2k)!}(f^{(2k-1)}(b)-f^{(2k-1)}(a))$$

can I neglet the series with Bernoulli numbers? Thanks, Anna.

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    i.e. can I: $ \int_{a}^{b}f(x)dx+\frac{f(a)+f(b)}{2}+\sum_{k=1}^{\infty}\frac{B_{2k}}{(2k)!}(f^{(2k-1)}(b)-f^{(2k-1)}(a))\sim \int_{a}^{b}f(x)dx+\frac{f(a)+f(b)}{2}$?2012-02-29
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    Unless you give us more information about the shape of (the derivatives of) $f$ that's impossible to answer.2012-02-29

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