2 replies to this topic

[Rantaro]

Tính tổng $S=\dfrac{C^0_{2013}}{1}+\dfrac{C^1_{2013}}{2}+\dfrac{C^2_{2013}}{3}+...+\dfrac{C^{2013}_{2013}}{2014}$

[Rantaro]

Mọi người giúp mình với. Đáp án trắc nghiệm là

 

A. $\dfrac{2^{2014}-1}{2014}$

 

B.  $\dfrac{2^{2014}-1}{2013}$

 

C.  $\dfrac{2^{2013}-1}{2014}$

 

D.  $\dfrac{2^{2013}-1}{2013}$

[chanhquocnghiem]

Tính tổng $S=\dfrac{C^0_{2013}}{1}+\dfrac{C^1_{2013}}{2}+\dfrac{C^2_{2013}}{3}+...+\dfrac{C^{2013}_{2013}}{2014}$

Ta có :

$S=1+\frac{2013}{1.2}+\frac{2013.2012}{1.2.3}+...+\frac{2013.2012...2.1}{1.2.3...2004}$

$\Rightarrow 2014.S=2014+\frac{2014.2013}{1.2}+\frac{2014.2013.2012}{1.2.3}+...+\frac{2014.2013.2012...2.1}{1.2.3...2004}$

$=C_{2014}^1+C_{2014}^2+...+C_{2014}^{2014}=2^{2014}-1$

$\Rightarrow S=\frac{2^{2014}-1}{2014}$ (đáp án $A$)

Edited by chanhquocnghiem, 29-11-2016 - 22:50.