Question

[Nguyễn Danh Huy]

1/1x3 + 1/3x5 + 1/5x7 + 1/7x9 

Answer 1

[nguyễn thị vy]

=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9) chia 2 

=(1-1/9)chia 2

=8/9 chia 2

=4/9

Answer 2

[Nguyễn An Ninh]

Đặt $A=\genfrac{}{}{0ex}{}{1}{1x3}+\genfrac{}{}{0ex}{}{1}{3x5}+\genfrac{}{}{0ex}{}{1}{5x7}+\genfrac{}{}{0ex}{}{1}{7x9}$

$2A=\genfrac{}{}{0ex}{}{2}{1x3}+\genfrac{}{}{0ex}{}{2}{3x5}+\genfrac{}{}{0ex}{}{2}{5x7}+\genfrac{}{}{0ex}{}{2}{7x9}$

$2A=\genfrac{}{}{0ex}{}{1}{1}-\genfrac{}{}{0ex}{}{1}{3}+\genfrac{}{}{0ex}{}{1}{3}-\genfrac{}{}{0ex}{}{1}{5}+...+\genfrac{}{}{0ex}{}{1}{7}-\genfrac{}{}{0ex}{}{1}{9}$

$2A=\genfrac{}{}{0ex}{}{1}{1}-\genfrac{}{}{0ex}{}{1}{9}=\genfrac{}{}{0ex}{}{8}{9}$

$A=\genfrac{}{}{0ex}{}{8}{9}.\genfrac{}{}{0ex}{}{1}{2}=\genfrac{}{}{0ex}{}{4}{9}$