Greatest Coefficient (1 Viewer)

[davidgoes4wce]

Had a look at the Grove Binomial theorem for the greatest coefficient and one of their examples uses the formula

Tk+1/Tk > 1

Had a look using the Warwick Marlin book which states that

Tk+1/Tk => 1 (greater than or equal to)

Which is right the 'greater than' sign or the 'greater than or equal to' sign?

 

[InteGrand]

Had a look at the Grove Binomial theorem for the greatest coefficient and one of their examples uses the formula

Tk+1/Tk > 1

Had a look using the Warwick Marlin book which states that

Tk+1/Tk => 1 (greater than or equal to)

Which is right the 'greater than' sign or the 'greater than or equal to' sign?

 

[davidgoes4wce]

thanks integrand. May I also ask what font are you using to write that text? It seems you may have written books, study guides in the past? Any links on where I could get my hands on to use that font style to write questions or solutions here in future?

 

[leehuan]

A short guide to LaTeX
Technically, the strong inequality is preferred. However, Grove, and even Pender (Cambridge textbook) use the weak inequality.

 

[davidgoes4wce]

Second question in regards to 'Greatest coefficient'

(2x-1)^5. The solution has +80 and -80 if someone could explain why there are two answers that would be great.

 

[leehuan]

Greatest coefficient only refers to the magnitude. The sign isn't what matters here. It's just like the one you posted in the marathon

I'm taking a guess in that T3 and T4 both have magnitude 80 or something here, or T2 and T3. Haven't bothered expanding it out.


It's like (1-x)^3 in this essence, rather than (1+x)^3