Question

исследовать ряд на сходимость

Answer 1

По  признаку Даламбера имеем.


$a_{n}=(frac{9n+1}{9n+8})^{n^2},; ; a_{n+1}=(frac{9n+10}{9n+17})^{n^2+2n+1}\\lim_{xto infty}frac{a_{n+1}}{a_{n}}= limfrac{(frac{9n+10}{9n+17})^{n^2}cdot (frac{9n+10}{9n+17})^{2n+1}}{(frac{9n+1}{9n+8})^{n^2}}=lim(frac{9n+10}{9n+17})^{2n+1}=\\=lim((1-frac{7}{9n+17})^{frac{9n+17}{-7}})^{frac{-7(2n+1)}{9n+17}}=e^{frac{-14}{9}}<1; to ; sxoditsya$