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
Which one of the following numbers are irrational ?
liq [111]

Answer: B and E are irrational numbers

5 0
3 years ago
The number of miles Ford trucks can go on one tank of gas is normally distributed with a mean of 350 miles and a standard deviat
kati45 [8]

Answer:

The probability that a randomly chosen Ford truck runs out of gas before it has gone 325 miles is 0.0062.

Step-by-step explanation:

Let <em>X</em> = the number of miles Ford trucks can go on one tank of gas.

The random variable <em>X</em> is normally distributed with mean, <em>μ</em> = 350 miles and standard deviation, <em>σ</em> = 10 miles.

If the Ford truck runs out of gas before it has gone 325 miles it implies that the truck has traveled less than 325 miles.

Compute the value of P (X < 325) as follows:

P(X

Thus, the probability that a randomly chosen Ford truck runs out of gas before it has gone 325 miles is 0.0062.

7 0
3 years ago
Complete the equation for the horizontal line that passes through (5, –7).<br><br> y =
KiRa [710]

Answer:

y = - 7

Step-by-step explanation:

The equation of a horizontal line is

y = c

where c is the value of the y- coordinates the line passes through.

The line passes through (5, - 7) with y- coordinate - 7, thus

y = - 7 ← equation of horizontal line

8 0
2 years ago
points) Thursday, September 2, 2021 01:55 PM EDT Andrew has nine fewer coins than Casey. Bob has three more than twice as many c
swat32

Answer:

Andrew: 131 coins Bob: 265 coins Casey: 145 coins

Step-by-step explanation:

3 0
2 years ago
SELECT ALL THAT APPLY. In a population of 250 students, 60% are Whites, 20% are Latinos, 15% are Blacks, and 5% others. In a pro
Sophie [7]

In a proportionate stratified sample of 120, there are 72 Whites, 24 Latinos, 18 Blacks and 6  others.

Proportionate Stratified Sample

A proportionate stratified sample is one in which the size of the strata in the sample is proportional to the size of the strata in the population; in other words, the chance of selecting a unit from a stratum depends on the relative size of that stratum in the population.

Calculating the Proportionate Stratified Sample

The given percentage of -

Whites = 60%

Latinos = 20%

Blacks = 5%

Strength of the sample = 120

⇒ Number of Whites = 60% of 120

= 0.6 × 120

=72

Number of Latinos = 20% of 120

= 0.2 × 120

=24

Proportionate Stratified Sample of Blacks and Others

Count of Blacks = 15 % of 120

= 0.15 × 120

= 18

Count of others = 5% of 120

= 0.05 × 120

6

Thus, in a Proportionate Stratified Sample of 120, 72 are Whites, 24 are Latinos, 18 are Blacks, and 6 are others.

Learn more about Proportionate Stratified Sample here:

brainly.com/question/20692763

#SPJ4

6 0
1 year ago
Other questions:
  • Ocean waves move in parallel lines toward the shore. The figure shows the path that a windsurfer takes across several waves. For
    5·1 answer
  • students at a cooking school made a super sized rectangular pizza for a class party Lupita cut the pizza into 3 equal pieces the
    14·1 answer
  • just look at the picture i’m confused, whoever gets it right gets a thanks and brainliest whatever that is lol
    6·1 answer
  • The coordinates below represent a triangle that was dilated. J(-3, -12) à J’(-2, -8) K(-6, -15) à K’(-4, -10) L(-9, -12) à L’(-6
    14·1 answer
  • У
    15·1 answer
  • 1/3a = −5 <br><br> What does a equal?
    11·1 answer
  • HELP PLEASE I NEED THIS QUESTION
    5·1 answer
  • A car requires 25 litres of petrol for covering a distance of 350 km how much petrol will be required by the car to cover a dist
    7·2 answers
  • A cylinder and its dimensions are shown in the diagram. Which measurement is closest to the lateral surface area of the cylinder
    6·1 answer
  • Help please thankssss
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!