Question

Use the root test to determine the convergence or divergence of the series. (if you need to use or –, enter infinity or –infinity, respectively. ) [infinity] 1 nn n = 1

Answer 1

The root test is Divergent, for given [infinity] 1 nn n = 1.

The foundation take a look at to research the restrict of the nth root of the nth time period of your collection. Like with the ratio check, if the restrict is less than 1, the series converges; if it is extra than 1 (together with infinity), the series diverges; and if the restrict equals 1, you analyze not anything.

The root check this collection is divergent. again, there is not too much to this series. therefore, with the aid of the root take a look at this collection converges clearly and hence converges. notice that we needed to maintain the absolute cost bars at the fraction until we would taken the limit to get the sign accurate

Root test requires you to calculate the value of R the usage of the components under. If R is greater than 1, then the series is divergent. If R is less than 1, then the series is convergent.

explanation:

If tan is series

if Lim n root (1) = l

if l =<1 than it is convergent

if l = > 1 than it is divergent

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