1 / 32 nha 

                        thank you

Thank nha!!! nhờ bạn mik được 10 điểm

reititiruit

ty từ tổ

Dùng máy tính đấy em ơi

Đặt biểu thức trên là A ta có:

A = \(\frac{1}{3}\)+ \(\frac{1}{6}\)+ \(\frac{1}{12}\)+ \(\frac{1}{24}\)+ \(\frac{1}{48}\)+ \(\frac{1}{96}\)

A x 3 = \(1\)+ \(\frac{1}{2}\)+ \(\frac{1}{4}\)+ \(\frac{1}{8}\)+ \(\frac{1}{16}\)+ \(\frac{1}{32}\)

A x 3 = \(1\)+ \(1\)- \(\frac{1}{2}\)+ \(\frac{1}{2}\)- \(\frac{1}{4}\)+ \(\frac{1}{4}\)- \(\frac{1}{8}\)+ \(\frac{1}{8}\)- \(\frac{1}{16}\)+ \(\frac{1}{16}\)- \(\frac{1}{32}\)

A x 3 = 2 - \(\frac{1}{32}\)= \(\frac{63}{32}\)

A = \(\frac{63}{32}\): 3 = \(\frac{63}{96}\)

bằng 1

Đặt \(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{96}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+.....+\frac{1}{192}\)

\(\Rightarrow A-\frac{1}{2}A=\frac{1}{3}-\frac{1}{192}\)

\(\Rightarrow\frac{1}{2}A=\frac{21}{64}\)

\(\Rightarrow A=\frac{21}{64}.2=\frac{21}{32}\)

\(\frac{95}{96}\)ko lý do

\(\left(\times-\frac{1}{5}\right):\left(\frac{1}{2}+\frac{1}{6}+\cdot\cdot\cdot+\frac{1}{110}\right)=\frac{1}{5}\)

\(\Rightarrow\left(\times-\frac{1}{5}\right):\left(\frac{1}{1\times2}+\cdot\cdot\cdot+\frac{1}{10\times11}\right)=\frac{1}{5}\)

\(\Rightarrow\left(\times-\frac{1}{5}\right):\left(1-\frac{1}{2}+\cdot\cdot\cdot+\frac{1}{10}-\frac{1}{11}\right)=\frac{1}{5}\)

\(\Rightarrow\left(\times-\frac{1}{5}\right):\left(1-\frac{1}{11}\right)=\frac{1}{5}\)

\(\Rightarrow\left(\times-\frac{1}{5}\right):\frac{10}{11}=\frac{1}{5}\)

\(\Rightarrow\left(\times-\frac{1}{5}\right)=\frac{1}{5}\times\frac{10}{11}\)

\(\Rightarrow\times-\frac{1}{5}=\frac{2}{11}\)

\(\Rightarrow\times=\frac{2}{11}+\frac{1}{5}\)

\(\Rightarrow\times=\frac{21}{55}\)

\(\left(x-\frac{1}{5}\right):\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)=\frac{1}{5}\)

\(\Rightarrow\left(x-\frac{1}{5}\right):\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{10\times11}\right)=\frac{1}{5}\)

\(\Rightarrow\left(x-\frac{1}{5}\right):\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)=\frac{1}{5}\)

\(\Rightarrow\left(x-\frac{1}{5}\right):\left(1-\frac{1}{11}\right)=\frac{1}{5}\)

\(\Rightarrow\left(x-\frac{1}{5}\right):\frac{10}{11}=\frac{1}{5}\)

\(\Rightarrow x-\frac{1}{5}=\frac{1}{5}\times\frac{10}{11}\)

\(\Rightarrow x-\frac{1}{5}=\frac{2}{11}\)

\(\Rightarrow x=\frac{2}{11}+\frac{1}{5}\)

\(\Rightarrow x=\frac{21}{55}\)

Vậy \(x=\frac{21}{55}\)