anonymous
  • anonymous
Find the sum of the first 20 even numbers. Write a sequence that shows the first 20 even numbers.
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
2+4+6+8+10+12+14+16+18+20+22+24+26+28+30+32+34+36+38+40= 422?
anonymous
  • anonymous
Possibly? Unless there's another part to this question that we're missing
madhu.mukherjee.946
  • madhu.mukherjee.946
The first 20 even numbers are: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,3... Gauss's method for the sum is as follows: The sum is: 2+4+6+8+10+12+14+16+18+20+22+24+26+28+3... 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.

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anonymous
  • anonymous
That copy/paste tho lol
anonymous
  • anonymous
thank you sooo much both of you
madhu.mukherjee.946
  • madhu.mukherjee.946
your welcome

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