Question

Tính  tổng sau một cách hợp lí :

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2017.2019}\)

Làm được t tick

Answer 1

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{1017.2019}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\)

\(=1-\frac{1}{2019}\)

\(=\frac{2018}{2019}\)

Answer 2

\(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+....+\frac{2}{2017\cdot2019}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\)

\(=1-\frac{1}{2019}=\frac{2018}{2019}\)

Answer 3

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2017.2019}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\)

\(=1-\frac{1}{2019}\)

\(=\frac{2019}{2019}-\frac{1}{2019}\)

\(=\frac{2018}{2019}\)

Answer 4

Đặt biểu thức trên là A,ta có:

A = \(\frac{2}{1.3}\)+\(\frac{2}{3.5}+\frac{2}{5.7}\)+...+\(\frac{2}{2017.2019}\)

A = \(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}\)+...+\(\frac{1}{2017}-\frac{1}{2019}\)

A = \(1-\frac{1}{2019}\)

A = \(\frac{2018}{2019}\)

Vậy giá trị của biểu thức là \(\frac{2018}{2019}\)

_Hok tốt_

Answer 5

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2017.2019}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\)

\(=1-\frac{1}{2019}\)

\(=\frac{2018}{2019}\)

Answer 6

\(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{2017.2019}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2019}\)

\(=1-\frac{1}{2019}\)

\(=\frac{2018}{2019}\)