You need to ask if converges.
I need to find radius of convergence and interval of convergence of
In d'Alembert feature I find radius like this
Radius is 1
If I try in Cauchy feature, I get same:
first square root
Radius is 1
Interval of convergence:
I take -1 and 1
I do check if diverge/converge:
here != means 'not even'
- Did I do task correct?
- it diverge or converge?
- How interval of convergence change because of divergence and convergence?
How does answer change because of that?
How would answer change if it converged with limit 1/2?
And how would answer change if it would converge with limit 2?
By the ratio test, the series converges where the limit , diverges where the limit is and inconclsive where the limit .
So all we can say at the moment is that the series is convergent when , because this is where the limit .
You will need to use a different test to test the endpoints.
Specifically for the case of when the series becomes , this is a p-series with . What do you know about p-series?
For the case of when the series becomes , what are the conditions for which Leibnitz's Alternating Series Theorem implies convergence?