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  • The coefficients of x^n in the expansion of (1 + x)^2n and (1 + x)^2n ~1 are in the ratio (a) 1 : 2 (b) 1 : 3 (c) 3 : 1 (d) 2:1

The coefficients of xn in the expansion of (1 + x)2n and (1 + x)2n ~1 are in the ratio
(a) 1 : 2                   
(b) 1 : 3                  
(c) 3 : 1
(d) 2:1

 

Answers (1)

The answer is the option (d) 2:1

2nCn is the coefficient of xn in the expansion of (1+x)2n

&2n-1Cn is the coefficient of xn in the expansion of (1+x)2n-1

\frac{^{2n}C_n}{^{2n-1}C_n}=\frac{\frac{\left ( 2n \right )!}{\left ( n \right )!n!}}{\frac{\left ( 2n-1 \right )!}{n!\left ( n-1 \right )!}}

= (2n)!n!(n-1)!/(2n-1)!n!n!

= 2n(2n-1)!n!(n-1)!/n!n(n-1)!(2n-1)!

= 2/1

= 2:1
 

Posted by

infoexpert22

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