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Natalija [7]
4 years ago
5

I got this problem from an old algebra book and I seem to have got a mental block with Part 2:

Mathematics
1 answer:
bija089 [108]4 years ago
4 0

Step-by-step explanation:

S = 1 + 3/2 + 5/4 + 7/8 + ...

½S = 1/2 + 3/4 + 5/8 + 7/16 + ...

Subtracting:

S − ½S = 1 + 3/2 − 1/2 + 5/4 − 3/4 + 7/8 − 5/8 + ...

Simplifying:

S − ½S = 1 + 1 + 1/2 + 1/4 + ...

Writing in summation form:

S − ½S = 1 + ∑ ½ⁿ⁻¹

½S = 1 + ∑ ½ⁿ⁻¹

S = 2 + 2 ∑ ½ⁿ⁻¹

Using formula for sum of a geometric series:

S = 2 + 2 (1 / (1 − ½))

S = 2 + 2 (2)

S = 6

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luda_lava [24]

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Learn more about percentage   from

brainly.com/question/843074

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5 0
1 year ago
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