Question

Prove that (a/b)^-n=(b/a)^n​

Answer 1

Hint: Use the binomial theorem.

This states that (a+b)n=∑k=0n(nk)an−kbk=an+bn+∑k=1n−1(nk)an−kbk.

Now, note that every term in the second sum is positive; this is because a, b, and the binomial coefficients are all positive. Therefore, (a+b)n=an+bn+ (sum of positive terms) ⩾an+bn.

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Answer 2

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