# Did you know if you add up all the numbers from 1 to 100 consecutively (1 + 2 + 3...) it totals 5050?

Well not quiet tho, i got 5051, try lets see.

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When you add a list of numbers, it does not matter in what order you add them. You can mix them up, the sum should always end up being the same (as long as you don't add one more than once).

1 + 100 = 101

2 + 99 = 101

3 + 98 = 101

...

49 + 52 = 101

50 + 51 = 101

The sum of all numbers from 1 to 100, should be the same as adding 101 to itself 50 times

By definition, this is the same as multiplying 101 by 50.

Since you are multiplying by a multiple of 10 (the number 50 ends with a zero),

then the total MUST end with a zero.

Thus, if your first answer ends with 1, it cannot be correct.

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As you can see, we have a total of 100 numbers, which we used to form 50 pairs (i.e., 100/2)

each pair adds up to 101 (= 100+1)

If you have to add all numbers from 1 to "n", you will have "n/2" pairs, each one adding up to "n+1"

The sum will be n(n+1)/2

Here, n=100

the sum is (100 * 101)/2 = 10100/2 = 5050

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• if you got 5051, then you entered one of the numbers wrong

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• General formula for that is n(n + 1)/2 which is 100*101/2 in this example.

If you liked finding that out for yourself, you might also like this:-

The sum of cubes of the first n consecutive natural numbers is equal the square of their sum.Here are two examples.

1 + 2 + 3 = 6, so, 1^3 + 2^3 + 3^3 = 36 = (1 + 2 + 3)^2

1 + 2 + 3 + 4 = 10, so, 1^3 + 2^3 + 3^3 + 4^3 = (1 + 2 + 3 + 4)^2 = 100

So you now have the power to add up the CUBES of all the numbers from 1 to 100.

See if you can do it.

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• S=1 + 2 + 3+4+5.................100

It is an AP

First term =1 common difference =1 Number of terms =100

Hence S=(100/2){2x1+(100-1)x1}= (50){2+99}= 50x101=5050

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• S = 101*50 = 5050

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• This is such a pointless statement

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• 1 + 2 + 3 + 4 + .... + 100

= 50(101)

= 5050

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• Adding up numbers quickly can be useful for estimation. Notice that the formula expands to this:

\displaystyle{\frac{n(n+1)}{2} = \frac{n^2}{2} + \frac{n}{2} }

Let’s say you want to add the numbers from 1 to 1000: suppose you get 1 additional visitor to your site each day – how many total visitors will you have after 1000

• you tell me.

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