Question

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

Answer 1

$cos^2pi sqrt{n^2+n}=frac{1+cos2pisqrt{n^2+n} }{2} rightarrow1; nrightarrowinfty$

$cos2pi sqrt{n^2+n}=cos2pi ncdot sqrt{1+frac{1}{n}}$