- #1

ProPatto16

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## Homework Statement

show whether [tex]\sum[/tex] (n+5)/(n

^{3}-2n+3) is convergant of divergant

## Homework Equations

limit comparison test, lim a

_{n}/b

_{n}= c where c > 0

## The Attempt at a Solution

a

_{n}is given

let b

_{n}= n/n

^{3}

so then:

lim

__(n+5)/(n__

^{3}-2n+3)n/n

^{3}

= lim (n+5)n

^{3}/ (n

^{3}- 2n + 3)n

= lim (n

^{4}+ 5n

^{3}) / (n

^{4}- 2n

^{2}+3n)

= lim (5n

^{3}) / (-2n

^{2}+3n)

now as n -> infinity, lim (5n

^{3}) / (-2n

^{2}+3n) -> -5n/2

and as n -> inifinity, -5n/2 -> -inifinity... therefore divergant? since c < 0??

feel free to tell me i have no idea. these things confuse me so much.