> #mathematics , #math > Find the sum to infinity of the geometric series: 16 + 8 + 4 + 2 + 1 ......
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Steven Eastern boy
more than 2 weeks ago

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.
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