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: 115°
Step-by-step explanation:
We should note that the sum of the angles that are in a triangle is equal to 180°, therefore we will add the angles given and equate them to 180°. This will be:
(8x - 5) + (2x) + (3x - 10) = 180
8x - 5 + 2x + 3x - 10 = 180
Collect like terms
8x + 2x + 3x = 180 + 5 + 10
13x = 195
x = 195/13
x = 15
The angles are:
8x - 5 = 8(15) - 5 = 120 - 5 = 115°
2x = 2(15) = 30°
3x - 10 = 3(15) - 10 = 45 - 10 = 35°
Therefore, the largest angle is 115°
The answer is quite simple after looking at it. 0.1 is a tenth. 72 is a whole number, so you would have 72 1/10. 1/10 is a tenth and 72 is still the whole number.
No sé, prueba 2,3,5,7,11,13....
Hay muchos números primos!
