Calc 2 Convergence Tests

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5 Terms

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Integral Test

let the series be a function that is positive, decreasing, and continuous:

  • if the limit of the sequence as x approaches infinity converges then the series converges

  • if the limit of the sequence as x approaches infinity diverges then the series diverges

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p-series

  • if the p > 1 the series converges

  • diverges otherwise

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direct comparison test

  • to show that a series converges we must compare it to a larger convergent series

  • to show that a series diverges we must compare it to a smaller divergent series

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limit comparison test

let a and b be 2 series with positive terms and limit of a/b = L:

  • if the limit > 0 and finite, then either both a and b converge or both diverge

  • if limit = inf and a converges then b converges

  • lf the limit = 0 and b convertes then a converges

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geometric series

  • if the ratio < 1 the series converges

  • otherwise the series diverges