summing series Watch
this is a worked example question and it says
notice that this is the sum 1^2 + 2^2 +......+n^2+.....+(2n)^2
with the first n terms subtracted
im being really thick and dont see how they got that could someone explain?
the terms underlined are the ones subtracted. all the terms above makes up the sum (of r^2) from r=1 to r=2n. the leftover sum is the sum (of r^2) from r=(n+1) to r=2n.
1/6 . 2n . (4n+1) . (2n+1)
and from n+1 to 2n is
1/6 . 2n . (4n+1) . (2n+1) - 1/6 . n . (2n+1) . (n+1)
=n/6 . (2(4n+1)(2n+1)-(2n+1)(n+1)
=n(2n+1)/6 . (8n+2-n-1)