- #1
ProPatto16
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Struggling with this topic! :(
got a couple of questions.
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
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).. that's integration by parts. so that's the imporper integral?
i don't know 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 that's right?
3) i have nothing in my textbooks about finding intevals. i don't know where to even start.
thanks for any help
got a couple of questions.
Homework Statement
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
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).. that's integration by parts. so that's the imporper integral?
i don't know 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 that's right?
3) i have nothing in my textbooks about finding intevals. i don't know where to even start.
thanks for any help