Question

Tính \(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{91\times93}\)

Answer 1

đặt A = \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{91.93}\) 

ta có:

A = \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{91.93}\) 

=> 2A = \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{91.93}\) 

=> 2A = \(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{91}-\frac{1}{93}\) 

=> 2A = \(\frac{1}{1}-\frac{1}{93}\) 

2A = \(\frac{92}{93}\) 

=> A = \(\frac{92}{93}:2\)

A = \(\frac{46}{93}\)

Answer 2

=1-1/3+1/3-1/5+1/5-1/7+.........+1/91-1/93

=>1-1/93=92/92

Answer 3

Cảm ơn các bạn nha!