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))