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Use the appropriate test to decide whether the following serie converges or not:
[tex]\sum \limit_{n=1} ^{\infty} \frac{3n^2 - 2n +1}{2n^2 + 5}[/tex]
[tex]\sum \limit_{n=1} ^{\infty} \frac{3n^2 - 2n +1}{2n^2 + 5}[/tex]
What about these ones:LeonhardEuler said:Try the n-th term test for divergence.
For a) can I just say this series does not converge as a_n does not tend to zero as n --> infinity but to 2/3 instead.LeonhardEuler said:When you look at b, you should see that for large n it behaves like [itex]\frac{1}{2n^2}[/itex]. What test will let you use that fact?
c) is pretty straght foward. When you see everything in with powers and factorials you should think of the comparison test or the root test.
d)Similar to b). The sin basically has no effect because the series that this looks like converges absolutely.