Find the sum of the first 20 even numbers.
Write a sequence that shows the first 20 even numbers.
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Possibly? Unless there's another part to this question that we're missing
The first 20 even numbers are:
Gauss's method for the sum is as follows:
The sum is:
That would take a while to type into a calculator (or do by hand) and you might make a mistake.
Gauss noticed that if you write that out again, underneath the original and in reverse:
2 +4 + 6+ 8+ 10+12+14+16+18+20+22+24+26+28+30+32+34+3...
40+38+36+34+32+30+28+26+24+22+20+18+16+... 8+ 6+ 4+ 2
Then looking at the numbers above and below eachother, and summing them in turn, you get:
(2+40) + (4+38) + (6+36) +...+ (36+6) + (38+4)+(40+2)
Sum the figures in brackets:
(42) + (42) + (42) + ... + (42) + (42) + (42)
They're all the same, and equal to 42.
We know there are twenty of them, so the sum of twice the original series can be quickly calculated as:
20 x 42 = 840.
So we can deduce that the sum of the first twenty even numbers is 840/2 = 420.