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What is the value of 5 minus 5 over 3 plus 5 over 9 minus 5 over 27?
Wiki User
∙ 6y ago
5 - 5/3 + 5/9 - 5/27 + ... = 5 + 5(-1/3)¹ + 5(-1/3)² + 5(-1/3)³ + ...
The required sum is an infinite GP with initial term a = 5, and common difference r = -1/3
As |r| < 1, the sum can be found from sum = a/(1 - r)
→ 5 - 5/3 + 5/9 - 5/27 + ...
= 5/(1 - (-1/3))
= 5/(1 + 1/3)
= 5/(4/3)
= 5 × 3/4
= 15/4
= 3¾
Wiki User
∙ 6y ago
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