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How do you get SUM for series S 1 2 3 n-1 n Equals S n n 1 2 I want to understand how the above formula is arrived at.?
Raj1a
To rewrite the formula that became a victim of character stripping: 1+2+3+...+n-1+n = n(n+1)/2 Here's an intuitive way of seeing why the formula is true (though it won't constitute a formal proof): Usually, you calculate an average by adding all the numbers in a list together, and dividing by how many numbers there are. This means that if you have the average, and multiply this by how many numbers there are, you'll get the sum. Because the series increases in constant steps, the average is halfway between the start (1) and the end (n): it's (n+1)/2. There are n numbers from 1 to n. So we multiply the average by how many numbers there are, we get the sum: n(n+1)/2. This isn't the way the formula is proved by mathematicians, because it's not very easy to make rigorous, but actual proofs of the formula don't give an intuition. The easiest ways to prove that the sum is n(n+1)/2 all rely on knowing the formula beforehand. For example, you can check that n(n+1)/2 is really n more than the sum of the first n-1 numbers, which is n(n-1)/2 by the same formula. This means that IF the formula works for n-1, it works for n too. This allows us to prove it works for all values, providing we can check it for one starting value, such as n=1.
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