Struggling with this topic!! :((adsbygoogle = window.adsbygoogle || []).push({});

got a couple of questions.

1. The problem statement, all variables and given/known data

1) Determine the value of the improper integral when using the integral test to show that

[tex]\sum[/tex]k/(e^k/5) is convergant

given answers are

a)50/e

b)-1/(5e^1/5)

c)5

d)5e

e)1/50e

2) determine whether [tex]\sum[/tex] (n+5)/(n^3-2n+3) is convergant or divergant

3) find interval of convergance of the series [tex]\sum[/tex]5(x-3)^n

3. The attempt at a solution

1) by integral test, f(x) = k/(e^k/5) = ke^(-k/5)

and the integral of that is [-1/5*ke^(-k/5)] -1/5*e^(-k/5).. thats integration by parts. so thats the imporper integral???

i dunno how to relate that to any of the answers

2) i multiplied top and bottom by n^2 and then limit of 1/n and all varieties is 0 so i end up with lim 0+0/n-0+0=0 so converges... i just needa check if thats right?

3) i have nothing in my textbooks about finding intevals. i dunno where to even start.

thanks for any help

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# Sequences and series

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