Question

Ratio test on
10n^3 *2^(n+4) /pi^n

Answer 1

My work so far:\[10 * \frac{ (n+1)^3 }{ n^3 } * \frac{2^{5} }{2^{n+4} } * \frac{ \pi^n }{ \pi^{n+1} }\]

Answer 2

n+1 * flip of n ....

Answer 3

\[\frac{10(n+1)^3 *2^{n+1+4}}{\pi^{n+1}}\cdot \frac{\pi^n}{10n^3 *2^{n+4}}\]
\[\frac{\cancel{10}(n+1)^3 *2^{\cancel{n+4}+1}}{\pi^{\cancel{n}+1}}\cdot \frac{\cancel{\pi^n}}{\cancel{10}n^3 *\cancel{2^{n+4}}}\]
\[\frac{(n+1)^3 *2}{\pi~n^3}\]

Answer 4

since this is a cubic/cubic, leading coeffs are the limit .... 2/pi

Answer 5

Yeah, I forgot to include the 10. Thanks!