MATHEMATICS

JAMB 2007 - Question 26

Mathematics 2007 JAMB Past Questions - Question 26: Find the sum to infinity of the series 2+3/2+9/8+27/32+.....

Find the sum to infinity of the series 2+3/2+9/8+27/32+.....
A:
B:
C:
D:
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Correct Answer

C

Explanation

Sum to infinity = a/1-r → a = 2, r = ¾2/1-3/4 = 2/¼ = 2 ᷀ ¼ = 2/1 X 4/16To find the sum to infinity of the series 2 + 3/2 + 9/8 + 27/32 + ..., we can observe that each term is a geometric sequence with a common ratio of 3/4.The first term, a, is 2, and the common ratio, r, is 3/4.The sum to infinity of a geometric series can be calculated using the formula:S = a / (1 - r)Substituting the values into the formula:S = 2 / (1 - 3/4)Simplifying:S = 2 / (1/4)S = 2 * 4S = 8Therefore, the sum to infinity of the series 2 + 3/2 + 9/8 + 27/32 + ... is 8.