# What is the Direct Comparison Test for Convergence of an Infinite Series?

This test is very intuitive since all it is saying is that if the larger series comverges, then the smaller series also converges, and if the smaller series diverges, then the larger series diverges.

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The Direct Comparison Test for convergence of an infinite series states that if the terms of a series ( \sum_{n=1}^{\infty} a_n ) are all nonnegative and can be bounded from above by the terms of a convergent series ( \sum_{n=1}^{\infty} b_n ), then ( \sum_{n=1}^{\infty} a_n ) also converges. Conversely, if the terms of ( \sum_{n=1}^{\infty} a_n ) are all nonnegative and are bounded from below by the terms of a divergent series ( \sum_{n=1}^{\infty} b_n ), then ( \sum_{n=1}^{\infty} a_n ) also diverges.

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