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What Is The Sum Of 1+2+3+4...+n?

Day 4,816, 09:00 • Published in Belgium South Africa

• by Bakakun

1+2=3 , 1+2+3=6 ,1+2+3+4=10, 1+2+3+4+5=15... we can continue like this. How can we calculate 1+2+3+4+....+n if n is an integer? Here is the answer

we can say that the sum of 1+2+3+4+.....+n equals to an integer like a
1+2+3+4+....+n= a Now also we can say n+.......4+3+2+1= a too
1+2+3+4+....+n + n+n-1+n-2+....+3+2+1= 2a. Then we got

n.(n+1)=2a if we divide with 2 each side , a=n.(n+1)/2

This method was invented by a very clever German Mathematician Gauss.