Question

sigma n=1 to infinity (10n +3)/(n2^n)
converge or diverge ?

Answer 1

converges like crazy

Answer 2

thank you could you please tell me the first step to solve it @satellite73

Answer 3

oh sorry
i would use the eyeball test

\[2^n\] is exponential grows way faster than the polynomial in the numerator
but you could use the ratio test probably if you want something more math teachery

Answer 4

\[a_n=\frac{10n+3}{n2^n}\]
\[a_{n+1}=\frac{10(n+1)+3}{(n+1)2^{n+1}}\]

Answer 5

find
\[\lim_{n\to \infty}\frac{a_{n+1}}{a_n}\]