Examples 4.2.14(c):
We have to check the limit superior of the expression
By our result on the limit of the n-th root sequence, the lim sup of this expression is 1/2. Hence, by the root test the above series converges absolutely.
We have to check the limit superior of the expression
By our result on the limit of the n-th root sequence, the lim sup of this expression is 1/2. Hence, by the root test the above series converges absolutely.