Test whether the following series converges:

This series diverges.

*Proof.* We use the comparison test with the known divergent series . First,

since for all . Therefore,

Thus, by the comparison test we have established the divergence of

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Stumbling Robot

A Fraction of a Dot
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Determine whether the series *∑ ((1 + n*^{2})^{1/2} – n) converges

Test whether the following series converges:

This series diverges.

*Proof.* We use the comparison test with the known divergent series . First,

since for all . Therefore,

Thus, by the comparison test we have established the divergence of