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Radius of convergence practice problems

Where a power series converges, found with the ratio test. 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{3^{- n} \left(x - 1\right)^{n}}{n} \).

Problem 7.46easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{\left(x - 2\right)^{n}}{n} \).

Problem 7.47easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} 5^{- n} \left(x + 3\right)^{n} \).

Problem 7.48easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{3^{- n} \left(x - 2\right)^{n}}{n^{2}} \).

Problem 7.49easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} 5^{- n} \left(x + 1\right)^{n} \).

Problem 7.50easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{\left(x - 3\right)^{n}}{n!} \).

Problem 7.51easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{\left(x + 1\right)^{n}}{n!} \).

Problem 7.52easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{x^{n}}{n!} \).

Problem 7.53easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{\left(x - 3\right)^{n}}{n^{2}} \).

Problem 7.54easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{\left(x - 2\right)^{n}}{n^{2}} \).

Problem 7.55easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} 5^{- n} \left(x - 3\right)^{n} \).

Problem 7.56easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{4^{- n} x^{n}}{n^{2}} \).

Problem 7.57easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{4^{- n} \left(x - 1\right)^{n}}{n} \).

Problem 7.58easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{2^{- n} x^{n}}{n^{2}} \).

Problem 7.59easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{\left(x + 3\right)^{n}}{n!} \).

Problem 7.60easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} 3^{- n} \left(x + 3\right)^{n} \).

Problem 7.106easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{5^{- n} \left(x + 3\right)^{n}}{n} \).

Problem 7.107easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{2^{- n} \left(x - 1\right)^{n}}{n^{2}} \).

Problem 7.108easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{\left(x + 2\right)^{n}}{n!} \).

Problem 7.109easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} 2^{- n} \left(x - 3\right)^{n} \).

Problem 7.110easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{\left(x - 1\right)^{n}}{n!} \).

Problem 7.111easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{4^{- n} x^{n}}{n} \).

Problem 7.112easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{5^{- n} \left(x - 2\right)^{n}}{n} \).

Problem 7.113easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \left(x - 3\right)^{n} \).

Problem 7.114easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} 3^{- n} \left(x + 2\right)^{n} \).

Problem 7.115easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} 4^{- n} \left(x + 1\right)^{n} \).

Problem 7.116easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} 5^{- n} x^{n} \).

Problem 7.117easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{4^{- n} \left(x + 3\right)^{n}}{n} \).

Problem 7.118easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \frac{\left(x - 2\right)^{n}}{n!} \).

Problem 7.119easy✓ Every equation proved

Find the radius of convergence of \( \displaystyle \sum_{n=1}^{\infty} \left(x - 2\right)^{n} \).

Problem 7.120easy✓ Every equation proved