Question

Using the comparison test to determine if the following is convergent or divergent:
Sum of [4(sqrt(n))-1]/(n^(5/4)+2n-1)

Answer 1

\[
\frac{4\sqrt{n}-1}{n^{5/4}+2n-1}
\]

Answer 2

The largest power in the numerator is 1/2 and that in the denominator is 5/4.
Therefore, this series will behave much like \[
\frac{\sqrt{n}}{n^{5/4}} = \frac{1}{n^{3/4}}
\]which diverges as a p-series with p <= 1 diverges.

Answer 3

thank you very much!

Answer 4

You are welcome.