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Rufina [12.5K]
3 years ago
8

A(n)

Mathematics
1 answer:
lianna [129]3 years ago
4 0

Answer:

Equation

Step-by-step explanation:

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Does the following infinite series converge or diverge? 1/3+2/9+4/27+8/81+...
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Note that A and D are ludicrous choices, so you can throw them away outright. (Any divergent series cannot have a sum, and any convergent series must have a sum.)

The sum is certainly convergent because it can be written as a geometric sum with common ratio between terms that is less than 1 in absolute value.

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\dfrac23S=\dfrac13\left(\dfrac23+\dfrac{2^2}{3^2}+\dfrac{2^3}{3^3}+\dfrac{2^4}{3^4}+\cdots\right)

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