\(B=\frac{1}{16}+\frac{6}{16.26}+\frac{6}{26.36}+\frac{6}{36.46}+...+\frac{6}{2006.2016}\) =\(B=\frac{1}{16}+\frac{3}{5}\left(\frac{10}{16.26}+\frac{10}{26.36}+\frac{10}{36.46}+...+\frac{10}{2006.2016}\right)\)

\(B=\frac{1}{16}+\frac{3}{5}\left(\frac{1}{16}-\frac{1}{26}+\frac{1}{26}-\frac{1}{36}+\frac{1}{36}-\frac{1}{46}+...+\frac{1}{2006}-\frac{1}{2016}\right)\)

\(B=\frac{1}{16}+\frac{3}{5}\left(\frac{1}{16}-\frac{1}{2016}\right)\)

đến đây thì ổn rồi

nhân với 1/6

nhân với 1/6 cả 2 vế rồi nhân cả 2 vế với 10

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

\(=\frac{6}{6.16}+\frac{6}{16.26}+\frac{6}{26.36}+....+\frac{6}{2006.2016}\)

\(=\frac{6}{10}\left(\frac{1}{6}-\frac{1}{16}+\frac{1}{16}-\frac{1}{26}+...+\frac{1}{2006}-\frac{1}{2016}\right)\)

\(=\frac{3}{5}\left(\frac{1}{6}-\frac{1}{2016}\right)\)

\(=\frac{67}{672}\)

\(B=\frac{1}{16}+\frac{6}{16\cdot26}+\frac{6}{26\cdot36}+...+\frac{6}{2006\cdot2016}\)

\(B=\frac{1}{16}+6\left(\frac{1}{16\cdot26}+\frac{1}{26\cdot36}+...+\frac{1}{2006\cdot2016}\right)\)

\(B=\frac{1}{16}+6\left[\frac{1}{10}\left(\frac{10}{16\cdot26}+\frac{10}{26\cdot36}+...+\frac{10}{2006\cdot1016}\right)\right]\)

\(B=\frac{1}{16}+6\left[\frac{1}{10}\left(\frac{1}{16}-\frac{1}{26}+\frac{1}{26}-\frac{1}{36}+...+\frac{1}{2006}-\frac{1}{2016}\right)\right]\)

\(B=\frac{1}{16}+6\left[\frac{1}{10}\left(\frac{1}{16}-\frac{1}{2016}\right)\right]\)

\(B=\frac{1}{16}+6\cdot\left[\frac{1}{10}\cdot\frac{125}{2016}\right]\)

\(B=\frac{1}{16}+6\cdot\frac{26}{4032}\)

\(B=\frac{1}{16}+\frac{25}{672}\)

\(B=\frac{57}{672}\)

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

\(B=\frac{1}{16}+6\left(\frac{1}{16.26}+\frac{6}{26.36}+...+\frac{6}{2006.2016}\right)\)

\(B=\frac{1}{16}+\frac{6}{10}\left(\frac{1}{16}-\frac{1}{26}+\frac{1}{26}-\frac{1}{36}+...+\frac{1}{2006}-\frac{1}{2016}\right)\)

\(B=\frac{1}{16}+\frac{6}{10}\left(\frac{1}{16}-\frac{1}{2016}\right)\)

\(B=\frac{1}{16}+\frac{6}{10}.\frac{125}{2016}\)

\(B=\frac{1}{16}+\frac{25}{672}\)

\(B=\frac{67}{672}\)

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

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

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

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

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

\(=\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{26}+...+\dfrac{1}{2006}-\dfrac{1}{2016}\)

=1/8-1/2016

=251/2016

nhanh lên ngày mai mk hk rùi

= 5/14

5/14 nha

\(\frac{5}{14}\)nha bạn