Please Help (Greatest Coefficient) (1 Viewer)

[Heresy]

Question is

Find the greatest coefficient of (2x - 1)^5.

I GET THE CONCEPT BEHIND GREATEST COEFFICIENT/ GREATEST TERM - However when you simplify this out (after factorials etc.) you will end up with -[6-k/2k].

1. As I go to solve for k, should I use T_{k +1} >1 or should I use T_k+1 < 1?


Also,

2. I keep on getting k<-6 when I use T_k+1 > 1, but when I use T_k+1 < 1 I get k>-6 - since k always has to be greater than or equal to 0 - where do I round it to?


Ik k is supposed to be 2 - I'm stuck on HOW to get there - I spent 1hr on this and still not done (please don't laugh) - Please Help!

 

[ichila101]

Solve for the greatest coefficient of (2x + 1)^5 instead and then you just need to ensure that k is an even integer so that the coefficient is positive since:
coefficient of T_k = 5Ck * (2)^(5-k) * (-1)^k for (2x - 1)^5

For (2x + 1)^5 you use the formula coefficients of T_k+1/T_k > 1 since all terms will be positive

 

[HeroWise]

I found this in the playground when i was playing with my 14 year old friends, might be useful