binomial methods (1 Viewer)

[sssona09]

hey guys, wondering how we find the greatest term and greatest coefficient in binomial expansion, using the general term

and what is the general term in terms of n and k?

for term independent of x, do we sub in 0 for x?

thank you!!!!!!

 

[tazhossain99]

General term for (x+a)^n : T_k= nCk X x^(n-k) X a^k
To find independent term: let n-k=0. If x is to the power of 0, then the whole term is independent of x (i.e. a constant)
Greatest Term: if T_(k+1) >= T_k, then k+1 yields the greatest term
Greatest Co-efficient: if t_(k+1) >= t_k, then k+1 yields the greatest term [t_k is just the coefficient of T_k i.e. t_k= nCk X a^k]

There will be a bit of manipulation and algebra required here and there when you are trying to find the independent term, greatest coefficient and greatest term.

Soz if this info does not look nice. I’m brain dead rn lol