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3.3 Worked examples

The audio provided below illustrates various methods for proving inequalities. In addition to the techniques already described for proving inequalities, we use mathematical induction and the Binomial Theorem, restated below.

Theorem 3.1 Binomial Theorem

  1. If x and n then

    (The notation is also denoted by nCk.

    By convention, 0! = 1, so Here, we also adopt the convention that 00 = 1.)

  2. If a, b x and n , then

Listen to the audio as you work through the frames.