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Find the infinite sum accurate to three decimal places. 2(-1)ⁿ 1/3ⁿ

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Answer: Sum is 1.5

Explanation:

This is a Geometric series, with common ratio : r = -1/3

The formula for the nth term is: a(sub n) = a(sub 0) * r^n, a(sub 0) is the first term

Here: a(sub n) = 2 * (-1/3)^n

Because |r| < 1, we can use the sum formula

S = a(sub 0) * (r^(n+1) - 1)/(r - 1)

n gets really big, so r^(n+1) = 0

S = a(sub 0) * (-1)/ (r - 1)

S = 2 * (-1) / ( -1/3 - 1)

S = 2 / (4/3) = 2*3/4 = 3/2

Infinite sum is 3/2 = 1.5

From MysticAlanCheng

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