I've come across the following summation(adsbygoogle = window.adsbygoogle || []).push({});

[tex]lim_{\stackrel{\Delta t \rightarrow 0}{n \rightarrow \infty}}\left(\Delta t \sum_{k=0}^n x^k\right)[/tex]

moreover, as [tex]\Delta t \rightarrow 0, x\rightarrow 1^-[/tex]

Does the sum converge? to what?

My thoughts....

The sum as [tex]n \rightarrow \infty [/tex] is simply the Mclaren series of [tex](1-x)^{-1}[/tex], so as [tex]x \rightarrow 1^- [/tex], the sum should diverge to [tex]+ \infty[/tex], however, we have the [tex]\Delta t[/tex] in the front that [tex] \rightarrow 0[/tex], and thats as far as my intellect takes me...

any ideas?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A sum I wish I never came across!

**Physics Forums | Science Articles, Homework Help, Discussion**