SOLUTION: What is the sum of all natural counting numbers from 1-9 inclusive

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Question 785568: What is the sum of all natural counting numbers from 1-9 inclusive
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I would add those 9 numbers twice and then divide by 2.
%28%281%2B2%2B3%2B4%2B5%2B6%2B7%2B8%2B9%29%2B%281%2B2%2B3%2B4%2B5%2B6%2B7%2B8%2B9%29%29%2F2
Rearranging them in pairs, matching them head to tail, I get nine sums added up
=
and each of them adds to 10
= %2810%2B10%2B10%2B10%2B10%2B10%2B10%2B10%2B10%29%2F2=9%2A10%2F2=9%2A5=highlight%2845%29

Your teacher will say that the sequence of numbers from 1 to 9 is an arithmetic sequence (or an arityhmetic progression, depending on where you go to school), and to apply formulas like
a%5Bn%2B1%5D=a%5Bn%5D%2Bd,
a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad
S%5Bn%5D=sum%28a%5Bi%5D%2Ci=1%2Ci=n%29=n%28a%5B1%5D%2Ba%5Bn%5D%29%2F2 and
S%5Bn%5D=sum%28a%5Bi%5D%2Ci=1%2Ci=n%29=%282a%5B1%5D%2B%28n-1%29d%29n%2F2
and that for the numbers from 1 to 9,
a%5B1%5D=1%2C+%7B%7B%7Bd=1, n=9, a%5B9%5D=9
If I had to deal with that, I would use
S%5Bn%5D=sum%28a%5Bi%5D%2Ci=1%2Ci=n%29=n%28a%5B1%5D%2Ba%5Bn%5D%29%2F2
and calculate
S%5B9%5D=sum%28a%5Bi%5D%2Ci=1%2Ci=9%29=9%281%2B9%29%2F2=9%2A10%2F2=highlight%2845%29
which is exactly what I did above (but without the formulas).