Evaluate- $$\lim_{n\to\infty}\sum_{r=1}^{n}\frac{1}{r!^{2}}$$. Is it possible to find the sum?Tried bringing it to integral form, using concepts of power series known to me, simplifying sum, but could not simplify. Will Stirling's Approximation be of use?
2026-04-08 17:05:30.1775667930
Infinite Factorial Sum
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Nothing is impossible, just believe on computational intelligence
$$\sum_{r=1}^\infty \frac{1}{(r!)^2}=I_0(2)-1\approx1.27959...$$here $I_n(z)$ is the Modified Bessel Function of the First Kind. More information can be found here.