What condition must be satisfied by an infinite geometric series in order for its sum to exist?
the absolute value of the common ratio must be less than $1$1
the common ratio must be negative
the common ratio must be less than $1$1
the common ratio must be greater than $1$1
the absolute value of the common ratio must be greater than $1$1
Consider the infinite geometric sequence $11$11, $22$22, $44$44, $88$88, $\text{. . .}$. . .
Consider the infinite geometric sequence $3$3, $-12$−12, $48$48, $-192$−192, $\text{. . .}$. . .
Consider the infinite geometric sequence $-40$−40, $-20$−20, $-10$−10, $-5$−5, $\text{. . .}$. . .