Riemann Sum Limit to Pi/2

1675AdeptCalculusSeries

Harvard-MIT Mathematics Tournament

For $n$ an integer, evaluate $$ \lim_{n \rightarrow \infty}\left(\frac{1}{\sqrt{n^{2}-0^{2}}}+\frac{1}{\sqrt{n^{2}-1^{2}}}+\cdots+\frac{1}{\sqrt{n^{2}-(n-1)^{2}}}\right) $$

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Riemann Sum Limit to Pi/2

1675AdeptCalculusSeries

Harvard-MIT Mathematics Tournament

For $n$ an integer, evaluate $$ \lim_{n \rightarrow \infty}\left(\frac{1}{\sqrt{n^{2}-0^{2}}}+\frac{1}{\sqrt{n^{2}-1^{2}}}+\cdots+\frac{1}{\sqrt{n^{2}-(n-1)^{2}}}\right) $$

0 students attempted0% solvedRating 1675