1. ## alg2

hey i need help with this one math problem in algebra 2
it says "find the sum of the numbers 1-500" now obviously they don't mean for you to begin adding numbers from 1-500 cuz that would take all year, anyone have any ideas on what they might want here? plz help if u can

2. Originally Posted by abarthle
hey i need help with this one math problem in algebra 2
it says "find the sum of the numbers 1-500" now obviously they don't mean for you to begin adding numbers from 1-500 cuz that would take all year, anyone have any ideas on what they might want here? plz help if u can
What they want is very clear. "Find the sum of the numbers from 1 up to 500."

It is also obvious that they don't mean we begin adding 1+2+3+4+5+..... up to +499+500.
They mean we use Math to "shortcut" the adding. And this "magic" is
(Sum from 1 to 500) = (500/2)(1+500) = 250*501 = 125,250. ------answer.

That is the value of an arithmetic series where the difference between any two consecutive terms of the series is one.
Difference between 2 and 1 is 1.
Between 436 and 437 is 1.
Between 94 and 93 is 1.

In books, the formula is Sn = (n/2)[a1 +an]
where
Sn = sum of all terms from a1 to an
a1 = first term
an = nth term
n = number of terms.

Now who said Math is boring?
Math is magic!

Try finding the sum of 1-9 using the formula. Then check what you get by adding 1+2+3+...up to 9.
There are 9 terms, so n = 9. First term is 1. nth term is 9.
Sum = (9/2)(1 +9) = (4.5)(10) = 45.

----------
To be more correct, the formula is
Sn = [(a1 +an)/2]*n
It is the middle term---or average of all the terms---that is multiplied by the number of terms.
But by the "magic" of Math, we can divide the n by 2 instead, and then multiply that by the sum of the first and last term, and we get the same answer. Magic.

Most of us take for granted the beauty of simple Math. Some thought the "higher" or "purer" the Math, the better.
Well, maybe.
For many, however, "simpler" Math is good enough. Or, better.

Analogy.
Most skilled workers in construction can build their own dwelling or improve or renovate what is existing.
Most supervisors, planners, engineers, managers, cannot.

3. Originally Posted by abarthle
hey i need help with this one math problem in algebra 2
it says "find the sum of the numbers 1-500" now obviously they don't mean for you to begin adding numbers from 1-500 cuz that would take all year, anyone have any ideas on what they might want here? plz help if u can
Here is a trick often attributed to C. F. Gauss as a small boy:

Write two copies of the sum out one above the other,
the first with the numbers in ascending order, the second
in descending order:

$\displaystyle \begin{array}{ccccc}1&+2&+3&... &+500\\500&+499&+498&... &+1\end{array}$

Now if we add the numbers in the first sum to the corresponding
number below them in the second we get:

$\displaystyle 501\ +\ 501\ +\ 501\ +\ ...\ +\ 501$,

in this sum there are now 500 501's to add, and obviously
we have added two copies of our original sum together.
Hence:

$\displaystyle 1\ +\ 2\ +\ 3\ +\ ...\ +\ 500\ =\ 500.501/2.$

RonL

4. alrite guys thank you very much