1. ## Greatest Term

When doing questions in binomial to find the greatest term, we first have to take a ratio of T(r+1)/T(r). But my question is that do we have to derive the ratio every time or can we just directly write T(r+1)/T(r)= (n-r+1)/r * b/a?

2. ## Re: Greatest Term

Originally Posted by Green Yoda
When doing questions in binomial to find the greatest term, we first have to take a ratio of T(r+1)/T(r). But my question is that do we have to derive the ratio every time or can we just directly write T(r+1)/T(r)= (n-r+1)/r * b/a?
I think it is safer to derive than to just cite the result formula.

3. ## Re: Greatest Term

It's usually 3 marks so derive but check with formula

4. ## Re: Greatest Term

Marks are given for the derivation, so it would be best to derive the ratio everytime

5. ## Re: Greatest Term

1 out of 3 at best if you use that formula.

6. ## Re: Greatest Term

The formula only works for simple single expansions. If you were to find the greatest term of something more complicated like (3+x)n+(1+2x)n you can't exactly use the formula. However, the principle of finding the largest value of k such that T(k+1)>T(k), where T(k+1) is general term of the entire expansion, is still valid (it will just look very different to your standard case).

7. ## Re: Greatest Term

Originally Posted by Trebla
The formula only works for simple single expansions. If you were to find the greatest term of something more complicated like (3+x)n+(1+2x)n you can't exactly use the formula. However, the principle of finding the largest value of k such that T(k+1)>T(k), where T(k+1) is general term of the entire expansion, is still valid (it will just look very different to your standard case).
In fact there was a past Ext 2 question requiring that method which had nothing to do with the binomial theorem. I think it involved exponentials.

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