Question

Decide convergence / divergence:
sum n=1 to infinity 1/(n*sqrt(n)+2)

Answer 1

converges for sure

Answer 2

since exponent in denominator is greater than 1

Answer 3

How to solve using comparison test or integral test?

Answer 4

integral test is just integrate from 1 to infinity

Answer 5

comparison is a limit of the ratio of ....
\[\frac{a_{n+1}}{a_n}\]

Answer 6

actually that is "ratio test"
comparison means compare to something else you know converges (or diverges)

Answer 7

of is the comparison a b_n of another ..... yeah lol

Answer 8

\[\sum_1^{\infty}\frac{1}{n\sqrt{n}+2}\]compare
\[\frac{1}{n\sqrt{n}+2}<\frac{1}{n^{\frac{3}{2}}}\] second sum converges