(a) Determine if the geometric series converges or diverges, and (b) if it converges, find its sum.
Answer
(a) The ratio r = 0.5 has magnitude less than 1, so this series converges.
(b) The first term is
a = (0.5)0 = 1.
The sum of the series is
(a) The ratio is r = -0.6. Since |r| < 1, this series converges.
(b) The first term of the series is
a = 2(-0.6)0 = 2.
a) The ratio is r = 2. Since |r| ≥ 1, this series diverges.
Hint
What is a?
(a) The ratio is r = 0.8. Since |r| < 1, this series converges.
(b) Since the sum starts at n = 5, the first term of the series is
a = 4(0.8)5 = 1.31072.
(a) The ratio is r = 1.2. Since |r| ≥ 1, this series diverges.
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