SOLUTION: find the sum of first n natural numbers

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Question 10615: find the sum of first n natural numbers
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
starting with first term of 1 (a=1) and incrementing by 1 (d=1), we have the following formula for an Arithmetic Progression/Series.

formula is S%5Bn%5D+=+%28n%2F2%29%2A%282a+%2B+%28n-1%29d%29

so, with a=d=1, we have: S%5Bn%5D+=+%28n%2F2%29%2A%282+%2B+%28n-1%29%29
S%5Bn%5D+=+%28n%2F2%29%2A%281+%2B+n%29

eg sum to 10 is S%5B10%5D+=+%2810%2F2%29%2A%281+%2B+10%29
S%5B10%5D+=+%285%29%2A%2811%29
S%5B10%5D+=+55

check... 1+2+3+4+5+6+7+8+9+10 is 55.

jon.