Lost on why he used 2.7 rather than 1.7, typo perhaps?

[mr_coffee]

Hello everyone I'm revewing a proof by strong mathematical induction and it seems to be making sense all the way up to this point:
Since (1.7)^2 = 2.98 > 2.7, we have...

WHy did he compare 1.7^2 > 2.7? we've been using 1.7 the whole time.



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Thanks!

 

[jpr0]

The 2.7 comes about because he factors out (1.7)^{k-2} from the following expression

<br /> (1.7)^{k-1} + (1.7)^{k-2} = (1.7)^{k-2}\left(1.7 + 1\right) = (1.7)^{k-2}(2.7)<br />

i.e. 1.7 + 1 = 2.7. He wants to make this statement about (1.7)^2&gt;2.7 so he can use it in the proof. Notice that in the penultimate step he uses an inequality (which assumes the above condition).

 

[mr_coffee]

Ahh i c it now, thank u for the help!