Furthermore, how can it be that the sum of any set of integers is not an integer. Even more, how can the sum of any set of positive numbers be negative? These two ideas lead me to think of inductive …

The first chapter of Concrete Mathematics by Graham, Knuth, and Patashnik presents about seven different techniques for deriving this identity, so you might be interested to look at that.

Sep 11, 2015 · Sum of first n natural numbers proof Ask Question Asked 10 years, 5 months ago Modified 4 years, 9 months ago

Nov 17, 2018 · Well, as I said before, string theorists need to use the sum of all natural numbers and if they use the value$\frac {-1} {12}$ they get accurate results (is what I have heard). And yes they are …

Now, the result does have meaning, but it is not literally that the sum of all naturals is -1/12. The methods they use to show the equality are invalid under the normal meanings of series convergence.

$P (n):$ the sum of the first $n$ odds is $n^2$. This is a proposition about the natural numbers; so we can now proceed to see if it can be proved by mathematical induction.

Think of pairing up the numbers in the series. The 1st and last (1 + n) the 2nd and the next to last (2 + (n - 1)) and think about what happens in the cases where n is odd and n is even.

Jan 10, 2018 · I do know how the sum of the first $n$ natural numbers using the Gaussian Method as a derivation, however, I am not sure even about the sum of the first $n^2$ natural numbers.

The price represented the sum of all future dividends, which were usually natural natural numbers, but could be anything that was positive. Prices were widely quoted, so if you had a price and Div1, which …

Apr 26, 2017 · Funny that you should use that method to demonstrate that the sum of all natural numbers is $-\frac {1} {12}$. I've seen the same claim demonstrated in a completely different way.