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## Main Question or Discussion Point

__Comparison Test__

Consider the two infinite series ##\sum a_n## and ##\sum b_n## with ##a_n,b_n \geq 0## and ##a_n \leq b_n## for all ##n##.

If ##\sum b_n## is convergent so is ##\sum a_n##.

If ##\sum a_n## is divergent so is ##\sum b_n##.

__Limit Comparison Test__

Consider the two infinite series ##\sum a_n## and ##\sum b_n## with ##a_n \geq 0## and ##b_n > 0## for all ##n##. Define:

$$c = \lim_{n \rightarrow \infty} \frac{a_n}{b_n}$$

If ##c## is positive and finite then either both series converge or both series diverge.

Does it matter if the two series we're comparing have different starting points? I don't think it matters because we can always strip out a finite number of terms from one of the series until both series have the same starting point.

http://tutorial.math.lamar.edu/Classes/CalcII/SeriesCompTest.aspx

But according to this link, "in order to apply this test we need both series to start at the same place."