An integral finds area under a curve. Since a series is adding rectangle areas, and an integral finds the curve's area, they should behave similarly.

That is the entire reason the Integral Test exists.

Conditions

To use the integral test, the series must be

1. Positive
2. Decreasing
3. Continuous

Solving

1. Identify f(x)
2. Check that it meets the conditions
3. Write the improper integral
4. Replace infinity with a variable
5. Integrate
6. Take the limit / plug in bounds
7. Match the conclusion to the series
   • The integral diverges, therefore by the integral test the series also diverges

• INTEGRATE FIRST, PLUG IN BOUNDS THEN TAKE LIMIT

Remainder Estimate