Thursday, 27 February 2014

discrete mathematics - Using Direct Proof. 1+2+3+ldots+n=fracn(n+1)2




I need help proving this statement. Any help would be great!


Answer



Here is an approach.



sn=1+2+3++(n1)+nsn=n+(n1)+(n2)++1.



Adding the above gives




2sn=(1+n)+(2+(n1))+(3+(n2))++(1+n)



=(1+n)+(1+n)++(1+n)



The above is nothing but adding (1+n) n times and the result follows



sn=n(n+1)2.


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