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+(n−1)+(n−2)+⋯+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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