I am solving for the stationary distribution whose state space is $S = ${$0, 1, 2,....$}. I need to calculate $ \frac{1}{\sum_{n=0}^{\infty} \frac{3^n}{n!}}$ for $ π(0)$. Then answer is $e^{-3}$, but I don't know how to get it.
2026-04-03 22:30:44.1775255444
How to calculate $ \frac{1}{\sum_{n=0}^{\infty} \frac{3^n}{n!}}$
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Note that $$ e^x=\sum_{n=0}^\infty\frac{x^n}{n!}. $$