use Gauss's approach to find the follwoing sums (do not use formulas).
a... 1+2+3+4+...+999
b... 1+3+5+7+...+997
the sum of sequance a is...
the sum of sequance b is...

Question

amistre64 · Answer

is there a reason they want you to add up the same number 1000 times?

anonymous · Answer

no. that's just what is it asking and I have no clue how to do it!

amistre64 · Answer

without a formula, then the only alternative would be by hand ....

anonymous · Answer

how would you do it??

amistre64 · Answer

by using the formula

dumbcow · Answer

haha ..i thought Gauss's approach was the formula ? he came up with the formula..allegedly

amistre64 · Answer

spose we do this on a smaller set:

{1,2,3,4,5}

add the set to itself, then we have twice as much in value.

{1,2,3,4,5} + {1,2,3,4,5} = 2{1,2,3,4,5}

amistre64 · Answer

if we add the set to itself in a convienent way we get:

{1,2,3,4,5}
{5,4,3,2,1}
----------
{6,6,6,6,6} ; or simply 5(6)  but this amount is twice the one we want, so divide it in half

amistre64 · Answer

why you would want to do that for 1000 terms is beyond me

anonymous · Answer

I did that for my problem, and it was wrong.

amistre64 · Answer

its just that simple for part a, for part b you have to determine how many terms there are ... there aint 997 of them

dumbcow · Answer

$$\text \sum = \frac{n(a_1 +a_n)}{2}$$

amistre64 · Answer

in part b, if we include the evens to fill out the set; we get from 1 to 998; we only want half of those terms; so n = 998/2 in that case

dumbcow · Answer

Gauss noticed that if you add the first and last number, and then the 2nd and 2nd to last number, you get same number

1+999 = 1000
2+998 = 1000
...

the number of pairs is 999/2
--> (999/2) *1000

anonymous · Answer

nope. just tried that and it's wrong.

dumbcow · Answer

im pretty sure its right
sum = 499,500

anonymous · Answer

The answer was 250,000. How.. I have no idea. I am so lost!!

anonymous · Answer

Try this one... 47+48+49+50...+134

dumbcow · Answer

https://www.wolframalpha.com/input/?i=sum+1+to+999

amistre64 · Answer

$$\frac{(134-46)(47+134)}{2}$$

anonymous · Answer

Thank you.. that's right. but so I understand, why use 46 and not 48, 49, or 50?

amistre64 · Answer

it starts at 47, its simpler to count the number of terms when they start at 1; 47-46 = 1

subtract the same amount from both ends

amistre64 · Answer

47 to 134
-46     -46
---     ----
    1 to   88 ; therefore there are 88 terms in the given sequence

amistre64 · Answer

of course im taking notice that each term is "1" from the next.

anonymous · Answer

ok.. i think i understand.. sort of