Euler's number/Interest estimates/Exercise

Show the following estimates.

a)

${}{\binom {n}{k}}\cdot {\frac {1}{n^{k}}}\leq {\frac {1}{k!}}\,,$

b)

${}{\left(1+{\frac {1}{n}}\right)}^{n}\leq \sum _{k=0}^{n}{\frac {1}{k!}}\,.$

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