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Absolute convergence, ratio and root tests

Absolute Convergence
  • If converges, then converges, and we say that the series converges absolutely.
Ratio Test
  • Let be any series and suppose that . Then (a) the series converges absolutely if , (b) the series diverges if , and (c) the test is inconclusive if .
Root Test
  • Let be any series and suppose that . Then (a) the series converges absolutely if , (b) the series diverges if , and (c) the test is inconclusive if .
If the expression in the interactive figure is too long to fit on the screen, you can drag it to see if more fully.
Developed for use with Thomas' Calculus, published by Pearson.