Greatest Term (1 Viewer)

[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?

 

[Drongoski]

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.

 

[pikachu975]

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

 

[fluffchuck]

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

 

[braintic]

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

 

[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).

 

[braintic]

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.