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Y12 Proof by induction question

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Reply 1
B3416316-26C5-4790-9778-B233950943A7.jpeg
D980A443-3D6E-4A21-B20F-62979709A674.jpeg

I was fine with the solution up until the third-to-last line. What exact change was made for the fourth-to-last line to become the third-to-last line? It wasn’t clearly explained in the solution.
(edited 7 months ago)
Reply 2
Original post by Sha.xo527
B3416316-26C5-4790-9778-B233950943A7.jpeg
D980A443-3D6E-4A21-B20F-62979709A674.jpeg

I was fine with the solution up until the third-to-last line. What exact change was made for the fourth-to-last line to become the third-to-last line? It wasn’t clearly explained in the solution.


Where's the question? Usually we assume it true for some n = k ... why do you hvae k + 1 in your assumption?
Original post by Sha.xo527
I was fine with the solution up until the third-to-last line. What exact change was made for the fourth-to-last line to become the third-to-last line? It wasn’t
clearly explained in the solution.


Ignoring the "-1"

(k+1)! + (k+1)(k+1)!

Separating out the factor (k+1)!
= (k+1)!(1+ (k+1))
=(k+1)!(k+2)

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