Ratio Test

THIS TEST IS GOOD FOR FACTORIALS.

▼Refer to xaktly: Ratio test / root test

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Example

Solve:

• Apply the ratio test:

  

• L = 0, so the series absolutely converges.

Example

Solve:

• Apply the ratio test, let a_(n+1) / a_n.

• The trick is to know: (n+1)! = (n+1)·n!, and (n+8)! = (n+8)·(n+7)!

• Take the limit to get:

  

• According to the ratio test, if L = 1, then there's no conclusion.