Question

How do you find the coefficient of `x^7" in "(1+x)^11`?

Answer 1

Reqd. co-eff. `""11C_7=330`.

Explanation:

In the Expansion of `(a+b)^n`, the `(r+1)^(th)` term, denoted by `t_(r+1)`, is given by,

`t_(r+1)=""nC_r*a^(n-r)*b^r.`

Letting `a=1, b=x, n=11`, we have, `t_(r+1)=""11C_r*1^(11-r)*x^r="11C_r*x^r`.#

As we need the co-eff. of `x^7`, we have to take `r=7`, giving the reqd. co-eff. `""11C_7=11C_(11-7)=""11C_4={(11*10*9*8)/(1*2*3*4)}=330`.