Monday, 31 March 2014

proof verification - Proving 0+2+4+cdots+(2n2)=n(n1) for all n inZ+




0+2+4++(2n2)=n(n1) for all n Z+



What I have:



Let n exist in Z^+. If n = 2, then L.H.S. = 2, and the R.H.S. = 2(2-1) = 2. So, L.H.S. = R.H.S. and this holds for n = 2. Assume this holds for some k existing in Z^+. That is 0 + 2 + 4 + ... + 2(k-2) = k(k-1)



What I am stuck on:



How do I show that this holds for 0 + 2 ... (2k-2) = k(k-1)?



Answer



You assume that for n=k, the statement holds:
0+2++2(k1)=k(k1).
You then want to prove the statement for n=k+1, that is, we want to show
0+2++2(k1)+2k=(k+1)k.



Can you make the connection from (a) to (b)?


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