Potentially useless

31
0
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.

Example:
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.
 
Hi

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.


Sridhar
 

ahrkron

Staff Emeritus
Gold Member
729
1
You can also think of it like this:

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

1+2+3+4+...+47+48+49+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
 

HallsofIvy

Science Advisor
41,626
821
"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.
 
31
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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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