Induction/3^n \geq n^4/Exercise/Solution

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Initial step for . We have

For the induction step let . Then

On the other hand the general binomial formula yields

We have to show

The first summands coincide on the left and on the right. For the other summands we show that the term on the left hand side, namely , is at least as large as the term on the right hand side. But this follows directly from (since ), from , since , from and from .