Root Test

"The root test is used in situations where a series term or part of it is raised to the power of the index variable. "

Notice: The root test isn't a good choice if a series contains factorial terms. If the root test isn't fairly easy to use, you probably shouldn't use it. But when it works, it often cuts to convergence or divergence quickly.

▼Refer to xaktly: Ratio test / root test

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Example

Solve:

• Apply the root test:

  
• Since L < 1, so it converges.