Question

Tính a)
\(B=\frac{1}{16}+\frac{6}{16.26}+\frac{6}{26.36}+\frac{6}{26.46}+.....+\frac{6}{2006.2016}\)

b) Cho x , y , z khác 0 và x - y - z = 0.Tính \(B=\left(1-\frac{z}{x}\right)\left(1-\frac{x}{y}\right)\left(1+\frac{y}{z}\right)\)
 

Answer 1

x-y-z=0=>x=y+z

=>z=x-y;=>y=x-z

\(=>B=\left(1-\frac{z}{x}\right)\left(1-\frac{x}{y}\right)\left(1-\frac{y}{z}\right)=\left(1-\frac{x-y}{x}\right)\cdot\left(1-\frac{y+z}{y}\right)\cdot\left(1+\frac{x-z}{z}\right)\)

Answer 2

Câu a cậu ghi sai đầu bài rồi hay sao í! phải là \(\frac{6}{36.46}\) chứ

Answer 3

Ta có x-y-z=0 suy ra x=z+y;y=x-z;-z=y-x

B=(1-z/x)(1-x/y)(1+y/z)

B=((x-z)/x)((y-x)/y)((z+y)/z)

B=(y/x)(-z/y)(x/z)

B=(-z.y.x)/(z.y.x)

B=-1