The+Integral+Test

 The Integral Test is a method to determine whether a particular type of series converges or diverges.

Suppose is a continuous, positive, decreasing function, and

1) If converges then converges 2) If diverges then diverges

Recall (p- test for improper integrals)



Diverges if p  1 Converges if p <span style="font-family: Arial,sans-serif;"> 1

<span style="font-family: Arial,sans-serif; line-height: 14.25pt; margin: 0in;">P series test



<span style="font-family: Arial,sans-serif;">Diverges if p <span style="font-family: Arial,sans-serif;"> 1 Converges if p <span style="font-family: Arial,sans-serif;"> 1

An example of the usage would be to try to determine whether the harmonic series converges or diverges: Harmonic series



,which diverges because p is equal to 1.