# The Third Number -Enigmatic Summation- (The Value of Zero)

Valerii Salov 11 2.

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## Summing Consecutive Numbers : qexefiducusu.tk

Alessandro's reasoning is good. Another way to get confidence in the answer is to view the positive integer n as n indistinguishable balls, which supposed to be placed into k distinguishable boxes so that some boxes can remain empty. By "well known", I mean, for instance, Riordan, John.

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An Introduction to Combinatorial Analysis. Princeton University Press, Like Objects and Unlike Cells.

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### Sum of n squares

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Of course Gauss came up with the answer about 20 times faster than the other kids. In general to find the sum of all the numbers from 1 to N: Hi Adam, Instead of the problem Dr. There must be an easier way!

## Summing Consecutive Numbers

A good way to approach such problems is to consider smaller problems and look for a patterm. Let's first ask, what is the sum of the digits ? What is the sum of the digits of the numbers ? We know that these numbers all have a "1" in the tens place, and a number in the units place. There are ten of these numbers, so there are ten 1's and the digits 0, 1, 2, 3, What about the sum of the digits of the numbers ?

Do you see the pattern?

So, when we add up the digits of all numbers , the expression is: