## 4.2. Convergence Tests

### Integral Test

Suppose that

Note that this test is much different from all the others. We have not
yet formally introduced the concept of an Integral - or even of a
continuous function - so that we can not prove this test here. However,
for completeness it is included as a test that is sometimes useful to
apply.
*f(x)*is positive, continuous, decreasing function on the interval*[N, )*. Let*a*. Then_{n}= f(n)converges if and only if converges