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.
Answer:
9 is the answer
Step-by-step explanation:
A _______ is a commonly accepted set of scientific ideas and assumptions.
Answer: paradigm
Answer:
70
Step-by-step explanation:
70 has the greatest absolute value because absolute value is the amount between that number and 0. If 70 is the biggest number the with the biggest absolute value is 70.
Answer:
slope is -5
Step-by-step explanation:
The formula for slope is:
m = (y2 - y1)/(x2 - x1)
m = slope
y2 = y-coordinate of second point
y1 = y-coordinate of first point
x2 = x-coordinate of second point
x1 = x-coordinate of first point
We can choose our first and second points as any points on the table, but we will choose the first andd second points which are (-5,10) and (-3,0).
y2 = 0
y1 = 10
x2 = -3
x1 = -5
m = (0-10)/(-3-(-5))
m = (-10)/(-3+5)
m = (-10)/(2)
m = -5
