Question

1.
Find the sum of the first 20 even numbers.

a.
Write a sequence that shows the first 20 even numbers.

b.
Use Gauss’ method to find the sum. Be sure to show and explain your work.

Answer 1

@BulletWithButterflyWings @AngelWilliams16 @abb0t

Answer 2

what do you mean first 20 even numbers

Answer 3

Nevermind that question :P I need the gauss method one ^_^

Answer 4

a. 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.

Hope that helps.

Answer 5

http://nrich.maths.org/2478

Answer 6

Thanks :P

Answer 7

Herro?

Answer 8

welcome