Summations Flashcards
How to use method of difference when they give just one fraction?
Use partial fractions to split apart and then find method of difference
How to leave it in fully factorised form
Add on the thing after factorising, expand, and then when done , collect and try FACTOISE AUADRATIC AGAIN
How to sum from another number to n?
Say from 2 to n, you want to sum from 1 to n subtrsvt all the numbers until 2, so you want 2 so do the number before
Thus it becomed sum 1 to n - sum from 1 to n-1!
And you can do this for anything even in algebraic form
And to work out the sum of the second one, just work out in terms of n and sub the VLAUE IN!
How to do partial fraction CUBIC OVER QAUDRATIC
It would split to be your quadratic x linear term when divindg
And you can sokit the quadratic up again by PARTIAL FRACTIONS
So it becomes ax + b + c / whatever + d / whatever
And this is how to solit
How to rig answer.
Make sure ti expand target and if = yours, then dont need to do more working out just rewrite in thst form and dien
How to do SEQUENCES
Prove true for n = 1 LHS is already given as u1 normally given
Then u1 sub into un to prove right hand side
2) assume true n =k easy
3) prove true for n=k+1 what you have to do is sub k+1 into un that’s what you’re tryna prove, and to prove it use the u n+1 and sub K INTO IT, and then expand snd collectterms
Rme,beer for indicided to add the powers
The BADES MUST BE THE SAME
so -2 not 2!
Finally for proof. Y induction now to always leave answer to show prof
Always leave in form where k+1 is SUBBED IN, this will confirm you’re correvt
How to do INDUCTION DIVISIBILITY
Show true for n = 1 easy
Assume true for n = k
- required you to make it =to whatver proof A, where A is a real positive integer
3) prove true
- put is k +1, and take the one out as indict
- rearrange the equation assumed for before somehow, sub back in
Show somehow you can take FACTOR OUT
And add Aconclusion LIKE NORMAL
What happens in the induction divisibility tests if rearranging doesn’t work
Take numbers out, replace what you expanded with with the assumptions will have to use assumption somehow , and then use techniques like consectibut numbers ALWAYS even etc !
