SOLUTION: Determine if the following series are convergent of divergent. If the series is geometric find the sum as well: [(-1)^n +1] / sqr n (NOTE: +1 is separated from ^n) at n =1 to

Question 579908: Determine if the following series are convergent of divergent. If the series is geometric find the sum as well:
[(-1)^n +1] / sqr n (NOTE: +1 is separated from ^n)
at n =1 to infinity

Thank you so much!

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
It is not a geometric series.
For odd n, (-1)^n=-1 and [(-1)^n+1]=0, so
For even n, (-1)^n=1 and [(-1)^n+1]=2, so .
In general, , so can be made less than any by just making . So it meets the definition of converging to zero.
However, the way you are expected to prove that it converges may be different.

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