tux Group Title Decide convergence / divergence: sum n=1 to infinity 1/(n*sqrt(n)+2) 2 years ago 2 years ago

1. satellite73

converges for sure

2. satellite73

since exponent in denominator is greater than 1

3. tux

How to solve using comparison test or integral test?

4. amistre64

integral test is just integrate from 1 to infinity

5. amistre64

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

6. satellite73

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

7. amistre64

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

8. satellite73

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