Thursday, November 14, 2019

Proof by induction help. I seem to be stuck and my algebra is a little rusty


Stuck on a homework question with mathematical induction, I just need some help factoring and am getting stuck.


1jnj3=[k(k+1)2]2


The induction part is: [k(k+1)2]2+(k+1)3 is where I am having a problem.


If you could give me some hints as to where to go since I keep getting stuck or writing the wrong equation.


I'll get to [k2+2k2]2+2(k+1)32


Any push in the right direction will be appreciated.


Answer



(k(k+1)2)2+(k+1)3


=k2(k+1)24+(k+1)(k+1)2


=(k+1)24(k2+4k+4)



=(k+1)24(k+2)2


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