Mathematics 2002 JAMB Past Questions - Question 25: The sum to infinity of the series 1/y +1/3+1/9+1/27+...... is

Correct Answer

D

Explanation

To determine the sum to infinity of the series 1/y + 1/3 + 1/9 + 1/27 + ..., we can observe that this is a geometric series with a common ratio of 1/3.The sum of an infinite geometric series can be calculated using the formula:S = a / (1 - r)where S is the sum, a is the first term, and r is the common ratio.In this case, the first term a is 1/y and the common ratio r is 1/3.Therefore, the sum to infinity of the series is:S = (1/y) / (1 - 1/3)  = (1/y) / (2/3)  = (1/y) * (3/2)  = 3 / (2y)Hence, the sum to infinity of the series 1/y + 1/3 + 1/9 + 1/27 + ... is 3 / (2y).