Mathematical induction

1. Apr 3, 2013

coconut62

Please refer to the image attached.

Where does the > 2 x k come from?

Based on the proposition, shouldn't it be > k+1?

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2. Apr 3, 2013

rbj

look two lines above the questioned statement.

3. Apr 3, 2013

coconut62

I got it, thanks.

4. Apr 3, 2013

coconut62

But one more thing: 2^(k+1) is equal or bigger than k+1. Then it's not necessarily bigger than k+1. How can we say that the proposition is true for that case?

5. Apr 3, 2013

Staff: Mentor

If k > 1, then 2k > k + 1.

2k = k + 1 only if k = 1.

6. Apr 4, 2013

Amir Livne

Greater and Greater-Equal

The propisition is true since it says $2^{k+1} > k + k \ge k+1$ and together $2^{k+1} > k+1$.