limn→∞(sin2n2+sin4n2+•••sin2nn2)=1 \lim_{n \to \infty}(\sin\frac{2}{n^2}+\sin\frac{4}{n^2}+•••\sin\frac{2n}{n^2})=1 n→∞lim(sinn22+sinn24+•••sinn22n)=1
∫04arctan4−x4+xdx=2 \int_{0}^{4}\arctan\sqrt{\frac{4-x}{4+x}}dx=2 ∫04arctan
limn→∞(sin2n2+sin4n2+•••sin2nn2)=1 \lim_{n \to \infty}(\sin\frac{2}{n^2}+\sin\frac{4}{n^2}+•••\sin\frac{2n}{n^2})=1 n→∞lim(sinn22+sinn24+•••sinn22n)=1
∫04arctan4−x4+xdx=2 \int_{0}^{4}\arctan\sqrt{\frac{4-x}{4+x}}dx=2 ∫04arctan