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JAMB Mathematics 1985 Question 14

Question 14

Indices

If ex = 1 + x + x2/1.2 + x3/1.2.3 + … Find 1/e½

  1. A.1 − x/2 + x2/1.23 − x3/24.3 + …
  2. B.1 + x/2 + x2/1.22 + x3/23.3 + …
  3. C.1 + x + x2/1.23 − x3/23.3 + …
  4. D.1 − x/2 − x2/1.2.3 − x3/1.2.3.4 + …
  5. E.1 + x2/1.2 + x3/1.2.4 + x4/1.2.6 + …
Show the answer and explanation

Answer: A (1 − x/2 + x2/1.23 − x3/24.3 + …)

Explanation

Replace x by −x/2 in the series: 1 − x/2 + (x/2)²/2 − (x/2)³/6 + … = 1 − x/2 + x²/8 − x³/48 + …, and 1.2³ = 8, 2⁴.3 = 48.