Algebra 2: Sequences and series: Sum of a geometric series

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12 Σ (1/2)^j , j goes from 1 to infinity

= 12[ 1/2+ (1/2)^2 +(1/2)^3 +......]

This is a geometric series with first term 1/2 and common ratio 1/2
= (1/2) / (1-1/2) = 1
(12)(1) = 12

the sum of an infinite decreasing geometric series is:

Σ = a/(1 - r)

where a is the first term and r is the common ratio.

for your series, a = 12 and r = 0.5

the sum is 12

check it...do the calculation.

@Σ