I ran across an infinite sum when looking over a proof, and the sum gets replaced by a function, however I'm not quite sure how.(adsbygoogle = window.adsbygoogle || []).push({});

$$\sum_{n=1}^\infty \frac{MK^{n-1}|t-t_0|^n}{n!} = \frac{M}{K}(e^{K(t-t_0)}-1)$$

I get most of the function, I just can't see where the ##-1## comes from. Could someone help show that?

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# I Series Expansion to Function

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