Gauss' method for addition relies on the fact that you can 'pair' certain numbers together. Look at the example:
1+2+3+4+5+6+7+8+9+10
We could manually add all these together from left to right but a clever way to think about this is if we add together the ends of the sum (10+1) we get 11. If we then move one in from the ends and add these (2+9) we also get 11. This means that 1+2+...+9+10 is the same as 11+11+...+11+11.
Because each 2 numbers adds to 11 we know the total number of 11's we have to add together is the length of the sum divided by 2. In our case 5 (10 ÷ 2). We need to add 5 lots of 11 to get our answer. This is the same as 11 × 5 which is easily seen to be 55.
(If you add the 10 numbers together on a calculator you'll see 1+2+3+4+5+6+7+8+9+10 = 55) so this method really makes it a lot quicker.
Looking at your sequence, if we pair the ends together we get 401 (400+1) and we multiply this by the length of the sequence divided by 2. In your case, 200 (400 ÷ 2).
So the sum of all the numbers from 1 to 400 must be 401 × 200 = 80,200.
Remember the steps:
1. Pair the ends together and add them
2. Times this number by the length of the sequence halved
Hope this helps.
-(7x + 4)- 2x + 2 = 52
Distribute the negative sign:
-7x -4 - 2x + 2 = 52
Combine like terms:
-9x - 2 = 52
Add 2 to both sides:
-9x = 54
Divide by -9:
x = -6
Answer: x = -6
Answer:
17/7
Step-by-step explanation:
2g+2(-8+2g)=1-g
2g-16+4g=1-g
6g-16=1-g
6g-(-g)-16=1
6g+g=1+16
7g=17
g=17/7
The commutative property of multiplication.
The answer would probably be 18 degrees below normal because the absolute values of the rest are 8 not 18 which is the absolute value of 18 degrees below normal.
