Wednesday, May 11, 2016

sequences and series - What must be the simplest proof of the sum of first n natural numbers?



I was studying sequence and series and used the formula many times 1+2+3++n=n(n+1)2 I want its proof.



Thanks for any help.


Answer



Let the sum be Sn=1+2+3++n on reversing the same equation we get Sn=n+(n1)+(n2)++1 On adding (1) and (2) we have each term equal to n+1 which will occur n times i.e. 2Sn=(n+1)+(n+1)+(n+1){ntimes}+(n+1) 2Sn=n(n+1) Sn=n(n+1)2. Hope it helps!!!


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