Artificial intelligent assistant

Find the digit in hundred-thousandth place of sum Sum: $1 + 3 + 9/2 + 27/6 + 81/24 + \ldots$ This is a problem on a competitive mathematics test, and I am trying to master the concept so I can understand when similar problems show up in future tests. Similar questions may ask for a digit in a different place, or a different type of sum, etc. Thanks

The Taylor series expansion of $e^x$ about $x=0$ is $$e^x = \sum\limits_{n=0}^{\infty} \frac {x^n} {n!},\ \text {for all }\ x \in \Bbb R.$$

Observe that your sum can be written as $$\sum\limits_{n=0}^{\infty} \frac {3^n} {n!} = e^3.$$

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