Mathematics 2000 JAMB Past Questions - Question 16: Evaluate (-1/2 -1/4+1/8-1/16+.....)-1

Correct Answer

C

Explanation

he expression you've provided is a sum of an infinite geometric series with the first term (-1/2) and a common ratio (-1/2). To evaluate this series, you can use the formula for the sum of an infinite geometric series: Evaluate (-1/2 -1/4+1/8-1/16+.....)-1 Evaluate (-1/2 -1/4+1/8-1/16+.....)-1 S = a / (1 - r)Where:S is the sum of the series.a is the first term of the series (-1/2).r is the common ratio (-1/2).Plugging in these values:S = (-1/2) / (1 - (-1/2)) S = (-1/2) / (3/2) S = (-1/2) * (2/3) S = -1/3So, the sum of the series is -1/3.To find the value of the expression (-1/2 - 1/4 + 1/8 - 1/16 + ...), subtract 1 from this sum:-1/3 - 1 = -1/3 - 3/3 = (-1 - 3)/3 = -4/3So, the value of the expression (-1/2 - 1/4 + 1/8 - 1/16 + ...) - 1 is -4/3.