Series Large
Series Large
What (if there is) the formula for the sum of a large series of consecutive numbers?
whether its 50, 500 or 10,000. Son took ‘Gaust(sp?)’ test last year in GR 7 it was last Q on test and I was sure there had to be a formula for it (btw he got it right 
Proud DAD
To compute 1+2+3+…+n-1+n without doing n-1 painful additions, just observe that you can pair the elements two by two by their distance to the extermity to get n/2 sums of n+1 (i.e. the first with the last one, the second with the one before last and so on). Hence the formula to compute the sum of the n first positive integers is f(n) = n(n+1)/2.
For instance, this yields 1+2+…+49+50 = f(50) = 50*51/2=25*51 = 5*5*51 = 255*5 = 1275, which you can do in your head.
Should you want to compute the sum of all consecutive integers between a and b, i.e. a+(a+1)+(a+2)+…+(b-1)+b, it is just f(b)-f(a-1)= b(b+1)/2 – (a-1)a/2
Hope it helps!
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