Question

Does the following series converge or diverge?
∑n=1∞[(n√)÷(n2+1)]

Answer 1

\[\sum_{n=1}^{\infty}[\left( \sqrt{n} \right)\div \left( n ^{2} + 1 \right)\]

Answer 2

Step 1: stop everything and download this flowchart: http://www.math.psu.edu/files/141seriesflowchart.pdf

It is from this page(full of more awesome resources)
http://www.math.psu.edu/ug/courses/math141

Answer 3

not really helping

Answer 4

Following the flowchart, we'd land at the comparison test. Try comparing \[\sum\frac{\sqrt{n}}{n^2+1} \text{less than or equal to ? }\sum\frac{\sqrt{n}}{n^2}\]

Answer 5

its less than

Answer 6

how do we know what it converges to?