Sunday, 3 August 2014

inequality - Induction prove beginequation2n2geqn!endequation for a nonnegative integer

Hi I submitted this as a graded assignment and received a poor grade. Could someone help me see what was wrong with my proof.



Let n be a nonnegative integer. Show that 2n2n!




Proof



(i) Base Case



For n = 0
We have 2020!
Which Yields, 11
Thus the base case holds.




(ii) Inductive Hypothesis:



Assume for some kZ,k0 that ,2k2k! then look at k+1



2(k+1)2=2k2+2k+1=2k222k2k!22k2 via inductive hypothesis




We now take k!22k2 and relate it to (k+1)!



k!22k2(k+1)!k!22k2(k+1)k!22k+1(k+1)



Thus the statement holds for k+1
Therefore by the generalized principle of mathematical induction,




2n2n! for nZ,n0

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