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Use partial sums to determine if the following series diverge or converge. If the series converges, determine its sum.
Σ (from n=0 to infinity) (2/(n^2 + 4n + 3)
 one year ago
 one year ago
Use partial sums to determine if the following series diverge or converge. If the series converges, determine its sum. Σ (from n=0 to infinity) (2/(n^2 + 4n + 3)
 one year ago
 one year ago

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satellite73Best ResponseYou've already chosen the best response.1
it definitely converges because the degree of the denominator is 2 and the degree of the numerator is 0 and the difference is greater than 1
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
to find the sum, i think the easiest thing to do would be partial fractions do you know how to do that?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
once you get the partial fraction, write out the first few terms and you will see that the sum "telescopes" that will not only give you a formula for the partial sums, it will also tell you what the infinite sum is
 one year ago

kd123Best ResponseYou've already chosen the best response.0
ok, thanks. Going to try it now.
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
write back if you get stuck, i will try it too
 one year ago

kd123Best ResponseYou've already chosen the best response.0
For the partial sums I got this
 one year ago

kd123Best ResponseYou've already chosen the best response.0
\[\frac{ 1 }{ 2 }+\frac{ 1 }{ 3 }\frac{ 1 }{n+2 }\frac{ 1 }{ n+3 }\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
if you are starting at \(n=0\) isn't the first term 1 ?
 one year ago

kd123Best ResponseYou've already chosen the best response.0
Oh yes you are correct. My mistake.
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
a small quibble, but it does make a difference i suppose
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
i get \(1+\frac{1}{2}\) and everything after that gets killed off
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
also i think ( i may be wrong about this) that for the partial sum you get \[\frac{3}{2}\frac{1}{n+3}\]
 one year ago

kd123Best ResponseYou've already chosen the best response.0
yes, I got this as well. Thanks for your help!
 one year ago

kd123Best ResponseYou've already chosen the best response.0
Can you help me again please. How do I go about doing this kind: \[\sum_{n=1}^{\infty}5(\frac{ 2 }{ 3 })^{n1} \] Use partial sums to determine if that series converges or diverges and if it converges, determine its sum.
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
geometric series for this one pull out the 5
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
\[5\sum_{k=0}^{\infty}(\frac{2}{3})^k\] use \[\frac{1}{1r}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
you can almost do it in your head \[1\frac{2}{3}=\frac{1}{3}\] the reciprocal of \(\frac{1}{3}\) is 3 and you get 15
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
yw again partial sums are a pain, but not too bad, it is just \[\frac{1r^n}{1r}\] in general
 one year ago

kd123Best ResponseYou've already chosen the best response.0
yeah, I'll try to remember that from now on :)
 one year ago
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