Question: Generalize Exercise 86; that is, use induction (if you are familiar with this method of proof) to prove that for all n 0, Exercise

Generalize Exercise 86; that is, use induction (if you are familiar with this method of proof) to prove that for all n ≥ 0,

1 ex > 1 + x + - x2 > 2 + + ... + 1 6 1 - n! (x > 0)


Exercise 86

Recall the following property of integrals: If ƒ(t) ≥ g(t) for all t ≥ 0, then for all x ≥ 0,

f* f(1)dt = f*g(1) dt z The inequality et  1 holds for t 0 because e > 1. Use (4) to prove that e 21+x for x

1 ex > 1 + x + - x2 > 2 + + ... + 1 6 1 - n! (x > 0)

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