Fichas
Method of Differences
Fichas del conjunto (4)
- 1How would we use the method of differences to work out (5Σr=1)(r+1)^3-r^3Sub in the values of r from 1 to 5 into the rule, so e.g. r=1 : (1+1)^3 - (1)^3, etc. Then cancel out as many terms as possible and one from the first row and one from the last should be left. Add/subtract these to find the sum.
- 2What would we change if using the method of differences to work out something like (nΣr=1)(r+1)^3-r^3As we don't know n, we would sub in values of r from 1 to 3 (or upto where we spot the pattern) and then sub in (n-2) ,
(n-1) and (n) and cancel out all terms, then add/subtract the 2 remaining to find the sum - 3Questions 1. Show that 1/2r-1 - 1/2r+1 = 2/4r^2-1 2. Hence find (nΣr=1)(2/4r^2-1) 3. Hence find (nΣr=1)(1/4r^2-1)1. (2r+1) - (2r-1) / 4r^2-1 = 2/4r^2-1
2. 2n+1/2n+1 - 1/2n+1 = 2n/2n+1
3. n/2n+1 as this is 1/2 of 2n/2n+1 - 4This video gives a deeper explanationhttps://www.youtube.com/watch?v=Z3uqs5fDOBM