Question

SA=1+2+3+4+5...500
SB= 501+502+503+...1000
(note: A and B are subscripts)
find s[B]+s[A]s/[B]−s[A]
(NOTE: A and B are subscripts)

Answer 1

Note what happens when u subtract the second one by the first

Answer 2

@pinkpony ?

Answer 3

wait... thats it?

Answer 4

you get 500

Answer 5

but both terms end with a different number.

Answer 6

Well, actually 500+500+500... And u should multiply 500 by 501 becuz I think that's how much times un have to add it

Answer 7

why though? maybe multiply sA numbers by 500?

Answer 8

this is arthmeric sequences by the way.

Answer 9

is this
\[\large \frac{S_A+S_B}{S_B-S_A}\]?

Answer 10

yes :)

Answer 11

then i think it is best to compute each number
do you know how to do that?

Answer 12

Becuz if u subtract the second equation by the first, u get 500+500+500... And u will eventually have 501 of these becuz that's how much terms u have, so ur denominator will be 500x501

Answer 13

\[s _{a}=1+2+3+4+5....500 s _{b}=501+502+503+....1000\]

Answer 14

what do you mean by compute?

Answer 15

\[1+2+3+...+1000=\frac{1000\times 1001}{2}=500\times 1001=500500\] for the numerator

Answer 16

i am really lost niko, this is not what I learned at school

Answer 17

And for the numerator, like u said, it's an arithmetic sequence
When u add both equations up, u get

502+504+506...1500

Answer 18

for the denominator
\[1+2+3+...+500=\frac{500\times 501}{2}=250\times 501=125250\]

Answer 19

and \[501+502+...+1000=500500-125250=500500-125250\]

Answer 20

why is there a two in the denominator? why is it being divided by two?

Answer 21

\[1+2+3+...+n=\frac{n(n+1)}{2}\]

Answer 22

your numerator is \(1+2+3+...+1000=\frac{1000\times 1001}{2}=500\times 1001=500500\)

Answer 23

@nikato omg i actually get what you mean now!!!!!!!!

Answer 24

\[S_A=+2+3+...+500=\frac{500\times 501}{2}=250\times 501=125250\]

Answer 25

why is times 501?

Answer 26

sorry for asking to many questions :P @satellite73

Answer 27

if \(n=500\) then \(n+1=501\)

Answer 28

doest his make more sense? this is what i was trying to say. but i wasnt really only a computer so i couldnt really show u

Answer 29

oh i see

Answer 30

so what do you do nexxt??

Answer 31

is there like some formula to do this?

Answer 32

u see how the SB equation is 1+2+3+4..500. so we know that there are 500 terms

Answer 33

uhaaa

Answer 34

which is the n...

Answer 35

so multiply 500 by 501 to get ur denominator. so this will represent if u actually subtract the second equation by the first equation

Answer 36

....and I am lost again

Answer 37

i get that...

Answer 38

lost? ur just muliplying 500 by 500 unless u want to add 500 500 times

Answer 39

denominator is \(500\times 500\) and the numerator is \(500500\) so i guess the best thing to do here is to divide