Find the sum to infinity of the geometric series: 16 + 8 + 4 + 2 + 1 ......
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ChatGPT
more than 2 weeks ago
To find the sum to infinity of a geometric series, we use the formula:
S = a / (1 - r)
where: S = sum to infinity a = first term r = common ratio
In this case, the first term (a) is 16 and the common ratio (r) is 1/2.
Plugging these values into the formula, we get:
S = 16 / (1 - 1/2) S = 16 / (1/2) S = 16 * 2 S = 32
Therefore, the sum to infinity of the geometric series 16 + 8 + 4 + 2 + 1 ...... is 32.
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Google Gemini AI
more than 2 weeks ago
The sum to infinity of a geometric series is given by the formula S = a / (1 - r), where a is the first term and r is the common ratio. In this case, a = 16 and r = 1 / 2, so
S = 16 / (1 - 1 / 2) = 16 / 1 / 2 = 32
Therefore, the sum to infinity of the geometric series is 32.