Q3 (c) --> mathematical induction question (1 Viewer)

cssftw

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So i didn't have much experience with inequality induction, I'd like to know what mark/3 I'd get, probs either 1 or 2/3.



Obviously I didn't know that 2k+1 > k+1 LOL

So is this 1/3 or 2/3? --> let's say I did forget to put in that final step of and just went on from the previous step straight to the conclusion -- 1/3 or 2/3?

thanks
 
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cutemouse

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2(k+1)! = ... >= (2k+2)(2k+1)2^k (k!)^2

= 2(k+1)(2k+1) 2^k (k!)^2
= (k+1)(2k+1) 2^(k+1) (k!)^2
>= (k+1)(k+1) 2^(k+1) (k!)^2 (as 2k > k for k>=1)
= 2^(k+1) ((k+1)!)^2, as required.

etc

Btw, this is really a 3U induction question...
 

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