Find out the answer to "White out explicitly and simplity as possible∑n=0n=5n2n!"

Kienastsrx

Answered question

2022-03-13

White out explicitly and simplity as possible

\sum_{n = 0}^{n = 5} \frac{n^{2}}{n!}

Summer Berg

Beginner2022-03-14Added 2 answers

Step1

\sum_{n = 0}^{n = 5} \frac{n^{2}}{n!}

Step2

\sum_{n = 0}^{n = 5} \frac{n^{2}}{n!}

= \frac{0^{2}}{0!} + \frac{1^{2}}{1!} + \frac{2^{2}}{2!} + \frac{3^{2}}{3!} + \frac{4^{2}}{4!} + \frac{5^{2}}{5!}

= \frac{0}{0} + \frac{1}{1} + \frac{4}{2} + \frac{9}{6} + \frac{16}{24} + \frac{25}{120}

= 0 + 1 + 2 + 1, 5 + 0, 67 + 0, 21

= 5, 38

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