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.



http://suprfile.com/src/1/3rop3a0/eee[/URL] copy.jpg[/PLAIN]



Thanks!

 

[jpr0]

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

$$(1.7)^{k-1} + (1.7)^{k-2} = (1.7)^{k-2}\left(1.7 + 1\right) = (1.7)^{k-2}(2.7)$$

i.e. $1.7 + 1 = 2.7$. He wants to make this statement about $(1.7)^2>2.7$ 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!