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

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Answer 1 · 2016-07-04T04:50:34

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

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. $""11C_7=11C_(11-7)=""11C_4={(11*10*9*8)/(1*2*3*4)}=330$ .

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