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JAMB Mathematics 1978 Question 7

Question 7

Progressions

The sum of the progression is 1 + x + x2 + x3 + . . . =

  1. A.1/(1 − x)
  2. B.1/(1 + x)
  3. C.1/(x − 1)
  4. D.1/x
  5. E.none of these.
Show the answer and explanation

Answer: A (1/(1 − x))

Explanation

This is a geometric progression with first term 1 and ratio x. For |x| < 1 the sum to infinity is a/(1 − r) = 1/(1 − x).