Just a "fairly innocent" infinite sum

We compute an infinite sum which looks like an innocent rational function but utilizes the digamma functions and its properties.
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Music by order:
birocratic & flamingosis - look both ways!

[@s1mpelness771]

That's a beautiful sum , Gamma function , Golden ratio 🤤, Literally best way to start your day !! , thank you

[@MayankSharma-oz2zp]

the answer is sqrt5 + 1 /10
easily done by telescoping

[@fahimnabeel606]

I dont know who your target audience is and maybe i am too dumb to understand but you should try to clarify thongs a bit more just make it feel a bit easier and natural, i dont know if you see bprp but his vid are really easy to catch and also you should not do the steps by just following the steps in your notes, it makes it feel a bit unnatural. Then again idk who your target audience is, i am just a uni student

[@nvapisces7011]

I am a uni student and I learn this in year 1. Using comparison test with the series 1/n, since 1/n is smaller than the given, and series of 1/n is a harmonic series, given series diverges