Nice "alternative" for calculating a Telescoping Series

[@antoinehedin6608]

Finally more straightforward than splitting the whole thing into two series expressed with the digamma function. Nice, as usual! 😊

[@owlsmath]

Ha! And yes I did consider that approach. 🤣 thanks!

[@antoinehedin6608]

Different ways leading to the same finish line ;-)

[@slavinojunepri7648]

Excellent telescoping method.
One small note:
The individual infinite sums diverge and strickly speaking cannot be used, though the result will be the same if partial sums were used instead.

[@owlsmath]

Ah that’s a good point! So technically I should show it all under one sum instead right?

[@slavinojunepri7648]

@owlsmath You could show it all under one infinite sum or separate partial sums.

[@MikeMagTech]

Very nice!

[@owlsmath]

thanks Mike! 👍

[@doronezri1043]

Perfecto👏👏👏

[@owlsmath]

thanks Doron! :)