Question

\(\left(1-\frac{2}{2.3}\right)\) X \(\left(1-\frac{2}{3.4}\right)\) X \(\left(1-\frac{2}{4.5}\right)\) X ... X \(\left(1-\frac{2}{99.100}\right)\)

Answer 1

\(\left(1-\frac{2}{2\times3}\right)\times\left(1-\frac{2}{3\times4}\right)\times\left(1-\frac{2}{4\times5}\right)\times...\times\left(1-\frac{2}{99\times100}\right)\)

=\(\frac{2}{2}-\frac{2}{3}+\frac{2}{3}-\frac{2}{4}+\frac{2}{4}-\frac{2}{5}+...+\frac{2}{99}-\frac{2}{100}\)

=\(\frac{2}{2}-\frac{2}{100}\)

=\(\frac{98}{100}\)

=\(\frac{49}{50}\)

Answer 2

\(=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}........\frac{9898}{9900}=\frac{1.4.2.5.3.6....98.101}{2.3.3.4.4.5.....99.100}=\frac{\left(1....98\right).\left(4...101\right)}{\left(2....99\right).\left(3....100\right)}=\frac{4}{2}=2\)

Answer 3

Bạn có thể ghi cụ thể ra không

Answer 4

cu thê đo bạn ;p

Answer 5

        \(\left(1-\frac{2}{2\times3}\right)\times\left(1-\frac{2}{3\times4}\right)\times\left(1-\frac{2}{4\times5}\right)\times...\times\left(1-\frac{2}{99\times100}\right)\)

= \(\frac{2}{2}-\frac{2}{3}+\frac{2}{3}-\frac{2}{4}+\frac{2}{4}-\frac{2}{5}+...+\frac{2}{99}-\frac{2}{100}\)

= \(\frac{2}{2}-\frac{2}{100}\)

= \(\frac{98}{100}\)

= \(\frac{49}{50}\)

Answer 6

      \(\left(1-\frac{1}{2\times3}\right)\times\left(1-\frac{1}{3\times4}\right)\times\left(1-\frac{1}{4\times5}\right)\times...\times\left(1-\frac{1}{99\times100}\right)\)

\(=\frac{2}{2}-\frac{2}{3}+\frac{2}{3}-\frac{2}{4}+\frac{2}{4}-\frac{2}{5}+...+\frac{2}{99}-\frac{2}{100}\)

 \(=\frac{2}{2}-\frac{2}{100}\)

\(=\frac{98}{100}\)

\(=\frac{49}{50}\)