Biz \(L\) ni hisoblashimiz kerak.

\[L = \mathop {\lim }\limits_{n \to \infty } \sqrt[n]{{\left| {{a_n}} \right|}} = \mathop {\lim }\limits_{n \to \infty } {\left| {\frac{{{{\left( { - 5} \right)}^{1 + 2n}}}}{{{2^{5n - 3}}}}} \right|^{\frac{1}{n}}} = \mathop {\lim }\limits_{n \to \infty } \left| {\frac{{{{\left( { - 5} \right)}^{\frac{1}{n} + 2}}}}{{{2^{5 - \frac{3}{n}}}}}} \right| = \left| {\frac{{{{\left( { - 5} \right)}^2}}}{{{2^5}}}} \right| = \frac{{25}}{{32}}\]

2-qadam

OK, biz \(L = \frac{{25}}{{32}} < 1\) va shunga o'xshash seriyani Root Test orqali ko'rishimiz mumkin birlashadi.