Evaluate (1/2 - 1/4 - 1/8 - 1/16 + ...) - 1

Assessment: JAMB UTME - Mathematics - 2000 Subject: General Mathematics

Question 1 Report

Evaluate (1/2 - 1/4 - 1/8 - 1/16 + ...) - 1
Answer Details
The given expression is a geometric series with the first term as 1/2 and the common ratio as -1/2. Using the formula for the sum of an infinite geometric series with |r| < 1, we can find that the sum of the series is: S = a/(1-r) = (1/2)/(1-(-1/2)) = (1/2)/(3/2) = 1/3 Therefore, the expression (1/2 - 1/4 - 1/8 - 1/16 + ...) - 1 simplifies to: 1/3 - 1 = -2/3 So, the answer is -2/3.

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