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# Integral Test for Convergence

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1.
Solution. Consider the integral

By the Integral Test, we know that converges.
Why do we choose 2 NOT 1? Since when we choose 1, then ln1=0. So,

2.
Solution. Since , we have

We know that diverges. So, by comparison test, we know that
diverges.

Method 2: The Integral Test

Consider a integral

So, diverges.

3. Use the Integral Test instead of known results of geometric series.

Solution. Consider the integral

So, by the integral test, we know that converges.

Also, we know it is a geometric series with |r|=1/e<1, so we know that converges.

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1.
Solution. Consider the integral

By the ...

#### Solution Summary

The Integral Test for Convergence is investigated. The geometric series in integrals are provided.

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