Question

[Lê Trường Giang]

a) ( 1+1/9) x ( 1+1/10 ) x ( 1+1/11) x .... x ( 1+1/120)

b) ( 1-1/10) x ( 1-1/11) x ( 1-1/12 ) x .... x ( 1-1/99)

Answer 1

[Mashiro Shiina]

Đặt:

\(X=\left(1+\dfrac{1}{9}\right)\left(1+\dfrac{1}{10}\right)\left(1+\dfrac{1}{11}\right).....\left(1+\dfrac{1}{200}\right)\)

\(X=\dfrac{10}{9}.\dfrac{11}{10}.\dfrac{12}{11}......\dfrac{201}{200}\)

\(X=\dfrac{10.11.12......201}{9.10.11......200}\)

\(X=\dfrac{201}{9}\)

\(Y=\left(1-\dfrac{1}{10}\right)\left(1-\dfrac{1}{11}\right)\left(1-\dfrac{1}{12}\right).....\left(1-\dfrac{1}{99}\right)\)

\(Y=\dfrac{9}{10}.\dfrac{10}{11}.\dfrac{11}{12}.....\dfrac{98}{99}\)

\(Y=\dfrac{9.10.11......98}{10.11.12.....99}\)

\(Y=\dfrac{9}{99}=\dfrac{1}{11}\)

Answer 2

[Lê Trường Giang]

Giúp mình với mai mình phải nạp cho cô giáo