Equations involving series Solve the following equations

Chapter 1, Problem 52RE

(choose chapter or problem)

Equations involving series Solve the following equations for x.

a. \(\sum_{k=0}^{\infty} e^{k x}=2\)               b. \(\sum_{k=0}^{\infty}(3 x)^{k}=4\)

c. \(\sum_{k=1}^{\infty}\left(\frac{x}{k x-\frac{x}{2}}-\frac{x}{k x+\frac{x}{2}}\right)=6\)

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