Root Test

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by stephaniejoy19
Last updated 4 years ago


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Root Test

This may be somewhat counterintuitive... How could anything raised to the nth power converge if n is approaching infinity?That's why it is important to know and be comfortable with these tests so that we can rely on them rather than our gut.

The test is different (obviously) but we interpret the results the same way as the ratio test.If the limit is less than 1, the series converges. If it is greater than 1, it diverges. If the limit equals 1, then we have no information.

Root Test

Even though the root test only applies to few series, and another test can usually be used successfully in its place, it is still handy to have in your toolkit - sometimes, if you notice that the root test applies, it is the fastest way to an answer.

Because the limit is 2/5 < 1, the root test immediately tells us that the series converges.

This is just further verifying the results of the root test by showing that the series does, in fact, converge.

If you don't remember this definition of e, don't sweat it... I am just reminding you because it comes up in the video.


The video below explains the test and shows three different examples. Pay attention to the second example if you struggle with algebra!


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