How I can show that $\sum _{n=1}^{\infty } \frac{1}{\sqrt{\Gamma \left(n^5\right)}}=1$ ? Any closed form?

Question

This question is related to my question here which it were related to irrationality inverse square root of Gamma function , I plug the following sum : $$\sum _{n=1}^{\infty } \frac{1}{\sqrt{\Gamma \left(n^5\right)}}$$in Wolfram Alpha with precision $30$ ,it returned the sum to exactly $1$, I have used The standard definition of $\Gamma(n) =(n-1)!$ trying to get its partial sum but it were complicated to me for evaluation, Now ,Is that sum interpreted any standard result ? and how I can evaluate it since it is rational ?

Answer 1

As mentioned in the comment section,

$$\sum _{n=1}^{\infty } \frac{1}{\sqrt{\Gamma \left(n^5\right)}} \neq 1.$$

Adding the first $10$ terms together, we get

$$1.0000000000000000110278059538310609032942060847778971258447535062193870006468053968418970017788817337127$$

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You can use Alpha to convince yourself.