A calculus problem by Bharath Sriraam

Calculus Level 4

Compute the value of the following infinite sum:

\[ \displaystyle \sum _{ r=1 }^{ \infty }{ \frac { { r }^{ 8 } }{ r! } } \]

NOTE

\( e =\displaystyle \lim_{x\rightarrow \infty} \left(1+\dfrac{1}{x}\right)^{x} \) is the Euler's number.

BONUS: Find \( \displaystyle \sum _{ r=1 }^{ \infty }{ \frac { { r }^{ n } }{ r! } } =?\)

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