Find r for each infinite geometric sequence identify any who

Find r for each infinite geometric sequence, identify any whose sum does not coverage.

12, 24, 48, 96, . . .

the answer is 2 and does not coverage.

Solution

r = any term/ previous term = 24/12 = 48/24 = 2

Sum of the series is given by = a/ 1-r = |2/( 1-2) |= 2

If |r| < 1 then the following geometric series converges to a / (1 - r).

If |r| >= 1 then the above geometric series diverges.