Given the sum(adsbygoogle = window.adsbygoogle || []).push({});

[tex]{_\lim {i} \rightarrow 0} \sum_{k=0}^{\frac{x}{i} - 1} i\sqrt{1 + i^{2n-2}((k+1)^{n} - k^{n})^{2}}[/tex]

I want to know how to derive to the value of this sum exactly. This is actually the value of the lenghts of a curve from a point to the origin of the form f(x) = x^n... I thought the binominal theorem can be used, but i can't develop on this further more. Anyone is capable of showing to what value this converges?

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# Value of a sum

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