Potentially useless

I found this scratching away on a peice of cardboard today. I thought I might troll the board and see what people think. Bare with me for I sometimes have trouble expressing whats in my head in words.

As follows:
Take the highest whole number median of an odd integer x and multiply it by said integer and the answer is equal to the sum of the counting number integers between 1 and x included 1 and x.

Assume x = 17
Highest median of 17 = 9
9 * 17 = 153
1+2+3+4+...+15+16+17 = 153

I've also found this works for even numbers assuming median + (1/2)(or -1/2 if integer x is negative).

Its a lot of blah blah blah and I don't see any applications, perhaps even missing something blatantly obvious(it is rather late after all). Share what you think. Thanks for reading.

What you have discovered is just this:

The sum of consecutive natural nos is n(n+1)/2. And the median is basically the middle value. And the sum of n natural nos satisfies this. I think ur discovery is evident from the formula. It is nothing new, but, anyway, a good observation. Keep Trying. All the Best.



Staff Emeritus
Gold Member
You can also think of it like this:

If you want to add, say, numbers 1 through 50:


you can rearrange them as follows:

(1+50) + (2+49) + (3+46) + ... + (25+26)

which are exactly 25 numbers, all equal to 51, hence, the sum is

51 * 25, or (50+1)*50/2


Science Advisor
"bare with me"??? Not likely!

You confuse things by talking about the "median" of a number.

Sets of numbers have medians, not individual numbers. Of course you meant the "median of the set of numbers 1, 2, ..., n". Of course, for a simple set like that, the median is the same as the mean. Pretty much by definition, multiplying the mean of a set of numbers by the cardinality of the set (I just could bring myself to write "the number of numbers in the set"!), n+1, gives you the sum of all the numbers.

If you had said "mean" instead of "median", it would have been obvious.
Thanks for your replies. Your posts remind me of the mathematical induction chapters in a few of my math books. I think my programming classes are overwriting the nerons in my brain.

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