1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
3241004551 [841]
3 years ago
7

Use the method of Gauss to find the sum.1+2+3+.....+400

Mathematics
1 answer:
nikklg [1K]3 years ago
6 0
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.
You might be interested in
Can someone help me with it? click on the photo to see it in full screen
dsp73

Answer:

Angie will need to save $2.50 for 8 more weeks to get $50

Step-by-step explanation:

Angie has already saved $30

12(2.5)=30

So since she needs $20 more you divide 20 by 2.5 and you get your answer.

20/2.5=8 weeks

6 0
3 years ago
HELP. PLEASE
tatuchka [14]
If we calculate the distance between two points, it is equivalent to one side of the rectangle. Using the distance formula:
d = √((x₂ - x₁)² + (y₂-y₁)²)
We compute the distance between the points (-3,2) and (5,4)
d = √((5 + 3)² + (4 - 2)²) = √68
Now, we check the next two points:
d = √((6 - 5)² + (0 - 4)² = √17
Now, we know that the adjacent sides of a rectangle are equal so the perimeter can be calculated using:
P = 2(l₁ + l₂)
P = 2(√68 + √17)
=24.7 units.
8 0
3 years ago
What is the solution of the equation 9 = -2x + 15?<br> A -21<br> B -12<br> C 3<br> D 12
Nataly [62]
I think the answer is c: three
7 0
3 years ago
Read 2 more answers
Please help me its really important
Serga [27]

Answer:

I think that the answer isssss B

5 0
3 years ago
Which of the following is equivalent to 3 (small) 4?<br><br> 7<br> 12<br> 64<br> 81
anygoal [31]
Do you mean 3^4?

If you mean this^ the answer would be 81.

4 0
2 years ago
Other questions:
  • If the day before yesterday was sunday.what day is one week from today?
    12·2 answers
  • 82- what number-33=35
    13·1 answer
  • Someone plz answer these <br> https://brainly.com/question/18427880
    14·2 answers
  • Find the area of the white region
    13·1 answer
  • Ajar contains 12 red balls, 7 green balls, 10 white balls, and 7 yellow balls.
    15·1 answer
  • Please help, i really need it
    12·2 answers
  • Choose Yes or No to tell whether each value of p is a solution for this inequality.
    7·1 answer
  • The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally injured
    13·1 answer
  • A male leopard seal is measured and has a length of 2.8 meters. A male elephant seal is about 1.5 times as long. What length is
    11·1 answer
  • 1. 3 tacos cost $18. Complete the table to show the cost of 4, 5, and 6 tacos at the same rate. Type the correct answer in each
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!