Multiple choice

Find an approximate value of $(0.99)$ $^5$ using the first three terms of its binomial expansion.

  1. $0.591$
  2. $0.951$
  3. $0.195$

  4. None
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B Correct answer
Explanation

(1 - 0.01)^5 = 1 - 5(0.01) + 10(0.01)^2 = 1 - 0.05 + 0.001 = 0.951.

AI explanation

Using the binomial expansion for (1 - 0.01) raised to the power of 5, the first three terms are 1 minus 5 multiplied by 0.01 plus 10 multiplied by 0.0001. Multiplying these out gives 1 minus 0.05 plus 0.001. Adding these three terms together results in 0.951. The approximate value of the expression is 0.951.

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