Oh Mighty Calculator

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like many people have done with their calculators, I was dividing 987654321 by 123456789. and I realized...

sum(0 to N) 987654321 * 10^(N*j)
divided by
sum(0 to N) 123456789 * 10^(N*j)

where N is any positive integer and j is in the real domain, there is a constant.


Am I weird and stupid?

Not at all. It's in your nature to see patterns and I see it as your strength. If you enjoy playing with numbers like this, I would encourage you to investigate this direction, even as an adjunct to a greater interest like physics, computers, or even something like statistics or research psychology.

In this case, since the multiplication will distribute across your summation (regardless of the magnitude of N), the net effect should be a cancellation of everything after the first "*" during the division process. This would lead to the appearance of a constant in this particular formula.

For the math purists:
Please pardon my inexact mathematical terminology . I know magnitude is typically used in vector calculus and that this may not technically be a formula in true "f(x)=" style per se... but in the interests of brevity and understandability I went this direction.

omg omg I'm so stupid.

something times (thing/thing) = something.

how can I be so stupid...

No no no no no! LOL... I do that all the time

If we never ask, we never learn! I don't know if I would have even seen the pattern like you did if I had been banging away on a calculator for so long. That's pretty brain-exhausting!

hope you dont mind me sort of hi jacking your thread but this is related due to it being calculator related.
Has anyone ever noticed that most statistics start with a 1 or 2 and then less and less 3s, 4s etc.

I have noticed that if you type into a calculator log(n+1)-log(n-1) *100 (made into a percentage)
(obviously n can not be zero because a statistic can not begin with zero)
You get the same percentage of statistics starting with 1 as when n=1 and same for 2 3 4 5 6 etc.

In order to get the statistics percentage you have to look through the back of an atlas or another reference book with maybe 8-1000 statistics, you may just want to trust me that they are the same.

Can anyone explain the trend?

what is the statistics percentage? a probability density?

log(n+1)-log(n-1) = log( (n+1)/(n-1) )
n > 1

The statistics percentage is meant to mean the percentage of statistics starting with a given number. Type my formula into your calculator and see what comes up, I was wondering if anyone could help me.