Chapter 8, Problem 64RE

a.

To determine

To solve: The equation ${\displaystyle \sum _{k=0}^{\infty }{e}^{kx}}=2$ for x.

b.

To determine

To solve: The equation ${\displaystyle \sum _{k=0}^{\infty }{\left(3x\right)}^k}=4$ for x.

c.

To determine

To solve: The equation ${\displaystyle \sum _{k=1}^{\infty }\left(\frac{x}{kx-\frac{x}{2}}-\frac{x}{kx+\frac{x}{2}}\right)}=6$ for x.