009C Sample Midterm 1, Problem 5

Find the radius of convergence and interval of convergence of the series.

a) $\sum _{n=0}^{\infty }{\sqrt {n}}x^{n}$

b) $\sum _{n=0}^{\infty }(-1)^{n}{\frac {(x-3)^{n}}{2n+1}}$

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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