Calculus Level 5

Define $$\displaystyle I_n(a)=\int_0^\infty \mathrm t^na^{-t}\,\mathrm{d}t$$ for positive real number $$\displaystyle a$$ and non-negative integer $$\displaystyle n$$.

Then find $$\displaystyle \sum_{n=0}^{\infty} \frac{1}{I_n(\pi)}$$ to two decimal places.

Try my other calculus challenges here

×