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.
<span>✡
Answer: x=6.72 </span><span>✡
- - Solve:
</span><span><span>- - First step is to cross-multiply:
</span>- </span><span>
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- - The next step is to divide both sides by the number </span><span>7.5
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</span>
<span>- - x=6.72</span>
✡Hope this helps<span>✡</span>
Answer:
Hope this helps
Step-by-step explanation:
The interior angles are 3, 4, and 6. Angle 3 is adjacent to angle 1, so is not remote.
The remote interior angles to angle 1 are
... A. angle 4
... E. angle 6
Answer:It would take 1.700 hours.
Step-by-step explanation:
