Question

\(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{99.101}\) = ?

 

Answer 1

\(=5.\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.100}\right)\)

\(=5.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(=5.\left(\frac{1}{1}-\frac{1}{100}\right)\)

\(=5.\frac{99}{100}=\frac{495}{100}=\frac{99}{20}\)

Answer 2

Đặt A = \(\frac{5}{1.3}+...........+\frac{5}{99.100}\)

suy ra A =  5(\(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}...........+\frac{1}{99}-\frac{1}{100}\))

suy ra A =  5(1-\(\frac{1}{100}\))

 

 

Answer 3

Gọi Tổng trên là A ta có :

\(A=\frac{5}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(A=\frac{5}{2}\left(1-\frac{1}{101}\right)\)

\(A=\frac{5}{2}. \frac{100}{101}\)

\(A=\frac{250}{101}\)