(2+4+6+...+2006)-(1+3+5+...+2005)

Question

I have the solution but it makes no sense. the answer is 1003. Can you twll me how to get the answer?

Answer 1

em thangs R kalled "arithmatik sequens"

2+4+6+...2006=2*(1+2+3+...1003)

sum av 1+2+3+...=n*(start number+last number)/2

step 1=figger out wot n be...it be 1003

step 2...sum=n*(start number+lastnumber)/2 or (n/2)*(start+last)

=(1003/2)*(1+1003)

but yu start with 2, so yer number=2*(1003/2)*(1004)=1003*1004=1,007,012

The other sequens...1+3+5+...sum=n^2=1003^2

so yu hav 1003*1004 -1003*1003

anser=1003