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?

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# A sum I wish I never came across!

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