Sum to Integral

[hollow moat]

What exactly is the goal here? If you're trying to calculate partial sums, there's a formula for that.

In any case, for the geometric series

$\sum_{k=0}^{n}ar^{k}$

you may treat $ar^{k}$ as an exponential function. The geometric sum would then just be the lower Riemann sum of that of function.

[bleak nymph]

solarunes

[timber basin]

https://www.youtube.com/watch?v=2pe1d31b8EM

[fallow token]

My actual goal is to prove the basel problem with integrals but before i convert a p-series into an integral I thought i should learn geometric series first because its easier to do.

I will watch the Video later but thanks a lot

[fickle agate]

Itd likely serve you better if you prove the basel problem using taylor series and weierstrass product series

[fallow token]

I already did that but my problem is that apparently i don't understand integrals as much as i thought i did so I thought it might help if i did a proof involving integrals and sums to understand it more about what their relationship is

[fickle agate]

Fair enough