# #\sum_(n=1)^\inftyn/(n^4+1)#?

##
I would use Comparison Test but apparently we have to go with the Integral Test. Any tips (it's apparently only supposed to take 2-3 steps)?

(btw, I assume this is an infinite series, but my terminology is rusty)

I would use Comparison Test but apparently we have to go with the Integral Test. Any tips (it's apparently only supposed to take 2-3 steps)?

(btw, I assume this is an infinite series, but my terminology is rusty)

##### 1 Answer

Converges by the Integral Test.

#### Explanation:

The Comparison Test would be the easiest option, but you can also use the Integral Test:

The Integral Test tells us if we have

If

Let

This is certainly continuous and positive on

So, the function is decreasing, we're good to use the integral test.

Let us first find the general indefinite integral:

Now, we want

So:

Since the improper integral has a finite value, it converges.

Then, by the Integral Test, so does the series.