Thursday 4 October 2018

sequences and series - Got this limit over here, been working on it for a while, thought it’s time to share it with you all




Got this limit I’d thought I should share it. So here you go:




$$\lim_{x\to\infty}{\bigg(\prod_{i=1}^{x}{\big(1+\frac{i}{x}\big)}\bigg)^{\frac{1}{x}}}$$




I have worked on this one for a while, with different angles and ended up with two different answers. Would like to see how you handled it.


Answer



Hint: Its logarithm is a Riemann sum.



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