What is 1 + 1 + 1 + 1 + ... ?

This is a geometric sequence with a ratio of 3/4.

This is also a geometric sequence. What is the ratio? (See part (b).)

This can be written as a telescoping sum:

$S=3\bigg(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...\bigg)$

$\text{ }=3\bigg(\Big(1-\frac{1}{2}+\Big(\frac{1}{2}-\frac{1}{3}\Big)+\Big(\frac{1}{3}-\frac{1}{4}\Big)+...\bigg)$