Hi,

I am asked to determine if the infinite sum of [1/5n - 1/(5n+3)] is convergent.

I tested each term individually and found that they both diverge, which means that I cannot say whether their difference converges or diverges.

Can anyone tell me what I should do when I encounter a difference or sum of series and they both diverge individually?

I found that the series above is greater than [1/5n^2 - 1(5n+3)] and that the first term in this converges while the second diverges still. So wouldn't that mean that their difference diverges, and that the original series diverges by the Comparison Test?

WolframAlpha says it converges ???

infinite sum (1/(5n)-1/(5n+3)) - Wolfram|Alpha

Any help? What should I do?

Thanks