1. Find the radius of convergence R and the interval of convergence C for each series. 2. Let R be the radius of convergence for the power series Σa n x n . If infinitely many of the coefficients an...

1. Find the radius of convergence R and the interval of convergence C for each series.

2. Let R be the radius of convergence for the power series Σa_nxⁿ. If infinitely many of the coefficients an are nonzero integers, prove that R ≤ 1.

3. Find the radius of convergence for each series.

4. Suppose that the sequence (an) is bounded but that the series Σa_n
diverges. Prove that the radius of convergence of the power series Σa_nxⁿ
is equal to 1.