Compute the value of the improper integral.

Question

Compute the value of the improper integral. (diverges to infinity, negative infinity or DNE).

∞

∫dx/4x =?

2

Use the answer to help determine whether the series :

∞

∑1/4n converges or diverges.

n=2

Answer 1

The integral diverges.

And so does the series.

The series ∑(1/n^p) converges for p strictly greater than 1 and diverges otherwise.