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1 + 2 + 3 + ... +n=1n (n + 1).2 |
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Answer» I have always liked this way. Write the series TWICE, with the SECOND TIME having the terms in reverse order. 1 + 2 + 3 + … + (n-2) + (n-1) + n n + (n-1) + (n-2) + … + 3 + 2 +1 Now add the two series together term by term. (n+1) + (n-1+2) + (n-2+3) + … + (3+n-2) + (2+n-1) + (1+n) = (n+1) + (n+1) + (n+1) + … + (n+1) + (n +1) + (n+1) You have added (n+1) a total of n times, so the sum is n(n+1). You added the series twice, so adding the series once will GIVE you n(n+1)/2 |
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