Question

Không quy đồng hãy tính hợp lí các tổng . Nhanh nha các bạn

\(\frac{2}{1.3}\)+ \(\frac{2}{3.5}\) + \(\frac{2}{5.7}\) +......+\(\frac{2}{99.101}\)

 

Answer 1

200/101

Answer 2

Ta có:\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+.............+\frac{2}{99.101}\)

\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+............+\frac{1}{99}-\frac{1}{101}\)

\(=1-\frac{1}{101}=\frac{100}{101}\)

Answer 3

Đặt \(A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)

\(\Rightarrow A=2\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{99.101}\right)\)

Đặt \(B=\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{99.101}\)

\(\Rightarrow2B=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(\Rightarrow2B=1-\frac{1}{100}=\frac{99}{100}\)

\(\Rightarrow B=\frac{99}{100}:2\)

Ta có : \(A=2B=\frac{99}{100}:2.2=\frac{99}{100}\)

Vậy tổng sau bằng \(\frac{99}{100}\)

Answer 4

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)

\(=1-\frac{1}{101}\)

\(=\frac{100}{101}\)

Answer 5

=2x99/101=198/101

Answer 6

\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)

\(\Leftrightarrow\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...\frac{1}{99.101}\)

\(\Leftrightarrow\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)

\(\Leftrightarrow1-\frac{1}{101}=\frac{100}{101}\)

Answer 7

con này mất dạy ah nha