Question

Вычислить предел $\displaystyle \lim_{n \to \infty} {\cos^{2}\pi \sqrt{n^{2} + n}}$

Answer 1

$cos^2\pi \sqrt{n^2+n}=\frac{1+cos2\pi\sqrt{n^2+n} }{2} \rightarrow1; n\rightarrow\infty$

$cos2\pi \sqrt{n^2+n}=cos2\pi n\cdot \sqrt{1+\frac{1}{n}}$