Question

Tinh

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right).......\left(1-\frac{1}{100}\right)+x=2+\frac{1}{5}\)

Answer 1

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)......\left(1-\frac{1}{100}\right)+x=2+\frac{1}{5}\)

\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}......\frac{99}{100}+x=\frac{11}{5}\)

\(\frac{1}{100}+x=\frac{11}{5}\)

\(x=\frac{11}{5}-\frac{1}{100}=\frac{219}{100}\)

Answer 2

đáp án bằng 2 ok

Answer 3

 X=219/100 đó nha!

chúc may mắn!!!

Answer 4

   \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)....\left(1-\frac{1}{100}\right)+x=2+\frac{1}{5}\)\(\frac{1}{5}\)

\(\Rightarrow\) \(\left(\frac{2}{2}-\frac{1}{2}\right)\left(\frac{3}{3}-\frac{1}{3}\right)\left(\frac{4}{4}-\frac{1}{4}\right)....\left(\frac{100}{100}-\frac{1}{100}\right)+x=\frac{10}{5}+\frac{1}{5}\)

\(\Rightarrow\)\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{99}{100}+x=\frac{11}{5}\)

 \(\Rightarrow\)\(\frac{1.2.3....99}{2.3.4....100}+x=\frac{11}{5}\)

\(\Rightarrow\)\(\frac{1.\left(2.3.4....99\right)}{\left(2.3.4....99\right).100}+x=\frac{11}{5}\)

\(\Rightarrow\)\(\frac{1}{100}+x=\frac{11}{5}\)

\(\Rightarrow\)\(\frac{1}{100}+x=\frac{220}{100}\)

\(\Rightarrow\)\(x=\frac{220}{100}-\frac{1}{100}\)

\(\Rightarrow\)\(x=\frac{219}{100}\)

Vậy \(x=\frac{219}{100}\)