To determine the convergence or divergence of a series using Root test, we evaluate a limit as:
or
Then, we follow the conditions:
a) then the series is absolutely convergent.
b) then the series is divergent.
c) or does not exist then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.
We may apply Root...
To determine the convergence or divergence of a series using Root test, we evaluate a limit as:
or
Then, we follow the conditions:
a) then the series is absolutely convergent.
b) then the series is divergent.
c) or does not exist then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.
We may apply Root test on the given series when we let:
.
Applying the Root test, we set-up the limit as:
Apply Law of Exponent: and
.
Evaluate the limit.
The limit value satisfies the condition:
since
.
Conclusion: The series is divergent.