Orchid XP v8 <voi### [at] devnull> wrote:
> >   Unfortunately not many people have that kind of deduction power at
> > that age (or at any age).

> For what it's worth, I can never ever remember *exactly* what the 
> correct formula for that is. It's roughly half the square, but I can 
> never remember the exact figure.

  You shouldn't memorize the formula (like most people do). You should
understand where it comes from (as I wrote in my previous post).

  Basically the general rule is: If you have to sum n numbers (whatever
those numbers might be), then summing the average of those numbers n times
with itself (or, in other words, multiplying the average by n) gives the
same result. If you think a bit about why this is so, it should be rather
simple.

  (Answer: The average of the numbers is calculated by summing the numbers
and dividing the result by n (which is the total amount of numbers). If you
multiply this average by n, you are nullifying the division, which gives you
the original sum.)

  With random numbers this rule doesn't help much (because calculating the
average of some random numbers would require you to sum those numbers
together, which was what you wanted to avoid doing in the first place), but
with consecutive numbers it does, because calculating the average of a
consecutive series of numbers can be done without having to all sum those
numbers.

  For example, the average of all the numbers between 1 and 100 (inclusive)
is (1+100)/2. Now just multiply that by the total amount of numbers, and
you have the sum.

  This same deduction works for any other ranges as well, even if the
numbers are not consecutive, as long as you can easily calculate their
average.

  Example: Calculate the sum of all the even numbers between 2 and 100
(inclusive).

  Answer: The average of all those numbers is (2+100)/2. The total amount
of even numbers in that range is 50, so multiply that average by 50, and
you got your result.

  Exercise: Calculate the sum of all the numbers between 100 and 1000
which are divisible by 7. (Obviously the range is non-inclusive because
neither 100 nor 1000 are divisible by 7.)

-- 
                                                          - Warp

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