Question

[Hoàng Thị Thanh Huyền]

Tính giá trị biểu thức:

\(A=\left(1+\frac{1}{2}\right)\times\left(1+\frac{1}{3}\right)\times\left(1+\frac{1}{4}\right)\times......\left(1+\frac{1}{2016}\right)\times\left(1+\frac{1}{2017}\right)\)

\(B=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+............+\frac{2}{43.45}\)

Tính bằng cách hợp lí:

\(\frac{2017}{2018}\)\(\times\)\(\frac{23}{47}\)\(+\)\(\frac{24}{2018}\)\(\times\)\(\frac{2017}{47}\)

\(=\)

\(=\)

\(=\)

\(=\)

Answer 1

[Hoàng Thị Thanh Huyền]

1    \(A=\left(1+\frac{1}{2}\right)\times\left(1+\frac{1}{3}\right)\times\left(1+\frac{1}{4}\right)\times.........\times\left(1+\frac{1}{2016}\right)\times\left(1+\frac{1}{2017}\right)\)

\(A=\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times......\times\frac{2016}{2017}\times\frac{2018}{2017}\)

\(A=\frac{2018}{2}=1009\)

\(B=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+.......+\frac{2}{43.45}\)

\(B=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-......+\frac{1}{43}-\frac{1}{45}\)

\(B=\frac{1}{3}-\frac{1}{45}\)

\(B=\frac{14}{45}\)

2     \(\frac{2017}{2018}\times\frac{23}{47}+\frac{24}{2018}\times\frac{2017}{47}\)

\(=\frac{2017}{2018}\times\frac{23}{47}+\frac{24}{47}\times\frac{2017}{2018}\)

\(=\frac{2017}{2018}\times\left(\frac{23}{47}+\frac{24}{47}\right)\)

\(=\frac{2017}{2018}\times1\)

=\(\frac{2017}{2018}\)

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