Greatest Co-efficient (1 Viewer)

[tempco]

tk+1/tk = (b/a) x [(n - k + 1)/k]

Ok to find the greatest co-efficient, my textbook states that the above equation is > 1. But I've seen several other questions which states that the above equation is < 1... when and why do you equate the equations to > 1 or < 1?

 

[Heinz]

Thats just the relationship between two consecutive terms. Obviously if a successive term is greater than its previous term, the ratio is > 1. Then you find the value of the term and check the value to the right of it and to the left of it to verify that it is the greatest term. so term 1 , term 2< ... < term 9 < term 10 (the greatest term) > term 11 > ... > term 19 > term 20 for example.

 

[tempco]

Ah ok... so it doesn't matter which you use, you just have to check it in the end to make sure it is the greatest co-efficient

 

[CrashOveride]

adding my random stupidity: ive seen stuff wher u hav less than or equal to...because sometimes they ask something and u have two terms for eg with the highest co-eff...this is like for questions where it goes what is the most likely number of successes. In that case we must check the rth+1 term and the rth term (for r some +ve integer) right? Sorry if i didnt make much sense...on the run

 

[psych_girl]

??

how can apply this?

 

[Li0n]

btw with that formula are you allowed to just apply it? or do you have to proove it whilst applying it?

 

[mojako]

btw with that formula are you allowed to just apply it? or do you have to proove it whilst applying it?

what formula?
I assume that this is a serious question
if not then...
I'll go invisible

Anyway,
1. It can be shown that the coefficients in the expanded form of (A+B)^n are increasing and then decreasing (and never increase again). Hence there's a peak where the coefficient is maximum. This can easily be seen from the pattern in Pascal triangle.
2. It can also be shown.. although I'm not exactly sure how and you don't have to know either (probably by inspection), that the terms in that expanded form, no matter what a is and what b is, are also increasing and then decreasing.

The statement 2 also implies that the coefficients of x-terms in the expansion of (ax+bx)^n are increasing and then decreasing, for whatever a and b.