Determine if series converges (mixed ln, sin and polynomials)

Question

$$\sum_{n=1}^\infty \frac{\ln^{5} (2n^{7}+13) + 10 \sin n}{n \ln^6 (n^{7/8} + 2 \sqrt n - 1) \ln (\ln (n + (-1)^{n}))}$$

I don't even know how to start, any hints how to solve so complicated sums?

Answer 1

HINT

Note that terms by term $\ln^5(2n^7+13) \approx \ln^5 n,|10 \sin n| \le 10, n^{7/8} + 2\sqrt{n} - 1 \approx n^{7/8}$ and $n + (-1)^n \approx n$.