Power series from the geometric series practice problems
Power series from 1/(1 − u) = Σ uⁿ: substitute, multiply, and read off the interval of convergence. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Find a power series for \( \displaystyle f(x) = \frac{2}{5 - x} \) centered at 0, and its interval of convergence.
Find a power series for \( \displaystyle f(x) = \frac{3}{1 - x^{2}} \) centered at 0, and its interval of convergence.
Find a power series for \( \displaystyle f(x) = \frac{x}{x + 1} \) centered at 0, and its interval of convergence.
Find a power series for \( \displaystyle f(x) = \frac{4}{5 - x} \) centered at 0, and its interval of convergence.
Find a power series for \( \displaystyle f(x) = \frac{x}{x^{2} + 1} \) centered at 0, and its interval of convergence.
Find a power series for \( \displaystyle f(x) = \frac{1}{2 x + 1} \) centered at 0, and its interval of convergence.
Find a power series for \( \displaystyle f(x) = \frac{2}{4 - x} \) centered at 0, and its interval of convergence.
Find a power series for \( \displaystyle f(x) = \frac{2}{1 - x^{2}} \) centered at 0, and its interval of convergence.
Find a power series for \( \displaystyle f(x) = \frac{1}{3 x + 1} \) centered at 0, and its interval of convergence.
Find a power series for \( \displaystyle f(x) = \frac{2}{x + 1} \) centered at 0, and its interval of convergence.