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Can I have an explanation regarding the notation "e" used here? Thank you :-)image link is in the below...]1

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    They just changed index of summation and use Taylor series.2017-01-08
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    This exact question was asked yesterday and was put off hold because it was lacking context. Can you provide some more context and explain where you are stuck? http://math.stackexchange.com/questions/2085766/how-to-prove-this-series-problem-sum-r-1-infty-fracr12r-5e-12017-01-08
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    @ElliotG : It is a considerable stretch to say that that is this exact question.2017-01-08
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    @MichaelHardy true but it appears to be the same person who keeps asking about this problem and they could have asked for clarification on the original post.2017-01-08
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    I could be wrong though.2017-01-08

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The number $e$ is the base of the natural exponential and natural logarithmic functions, which is $$ e = \sum_{n=0}^\infty \frac 1 {n!} \approx 2.71828182846\ldots $$