Question Number 103826 by bobhans last updated on 17/Jul/20

In the expansion of (1+x)^(20) if the coefficient of x^r is twice the coefficient of x^(r−1) , what the value of the coefficient?

Answered by bramlex last updated on 17/Jul/20

(1+x)^(20) = Σ_(r = 0) ^(20) C _r^(20) 1^r .x^(20−r) coefficient of x^r is (((20)),(( r)) ) and coefficient of x^(r−1) is ((( 20)),(( r−1)) ) so condition in equation (((20)),(( r)) ) = 2 ((( 20)),(( r−1)) ) note ((n),(r) ) = ((n−r+1)/r) ((( n)),((r−1)) ) so your equation reduces to ((20−r+1)/r) = 2 ⇒ r = 7. therefore the value of coefficient ((20!)/(7!.13!)) = ((20.19.18.17.16.15.14)/(7.6.5.4.3.2.1))