009C Sample Midterm 2, Problem 4

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

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

b) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum_{n=0}^\infty \frac{(x+1)^n}{\sqrt{n}}}

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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