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I need reference to a result on alternating series which I am remember vaguely and I am unable to find in Google because perhaps I am not searching for the right thing. It was somethign like this.

Instead of summing an infinite alternating series, we can truncate it at some point and the result said that if we truncate it at that particular point, the sum is a good enough approximation of the complete sum.

If I remember correctly, I had seen it in mathworld.wolfram. but ow, I am unable to find it again. Any reference to it will be very helpful.

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No reference at hand, but it is easy to see that if $a_n \rightarrow 0$, from one $n$ on the value can't oscilate by more than $\pm \epsilon$, so it has to converge. – vonbrand Feb 3 '13 at 20:09

Here's one:

The remainder has the same sign as the first omitted term and is bounded by its absolute value.

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