Question

[minny honoka]

C] [ X-1/2 ] CHIA [ 1/2 CONG 1/6 CONG 1/12 CONG 1/20 ] = 1/3

Answer 1

[Huỳnh Quang Sang]

c) \(\frac{x-\frac{1}{2}}{\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}}=\frac{1}{3}\)

Đặt \(S=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\)

\(S=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}\)

\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{4}-\frac{1}{5}\)

\(S=1-\frac{1}{5}=\frac{4}{5}\)

Do đó \(\frac{x-\frac{1}{2}}{S}=\frac{1}{3}\)

=> \(x-\frac{1}{2}=\frac{1}{3}S=\frac{1}{3}\cdot\frac{4}{5}=\frac{4}{15}\)

=> \(x=\frac{4}{15}+\frac{1}{2}=\frac{23}{30}\)