Question

[jiewer]

A=2/1.3+2/3.5+2/3.7+....+2/2021.2023

=)

B=1/2.5+1/5.8+1/8.11+...+1/95.98

Answer 1

[Ngô Hải Nam]

\(A=\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{2021\cdot2023}\)

\(A=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2021}-\dfrac{1}{2023}\)

\(A=\dfrac{1}{1}-\dfrac{1}{2023}\\ A=\dfrac{2023}{2023}-\dfrac{1}{2023}\\ A=\dfrac{2022}{2023}\)

Answer 2

[Đinh Trí Gia BInhf]

$A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{97.99}$

$A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{97}-\frac{1}{99}$

$A=\frac{1}{1}-\frac{1}{99}$

$A=\frac{98}{99}$

=

$\genfrac{}{}{0ex}{}{1}{2}-\genfrac{}{}{0ex}{}{1}{5}+\genfrac{}{}{0ex}{}{1}{5}-\genfrac{}{}{0ex}{}{1}{7}+....+\genfrac{}{}{0ex}{}{1}{95}-\genfrac{}{}{0ex}{}{1}{98}$

$=\genfrac{}{}{0ex}{}{1}{2}-\genfrac{}{}{0ex}{}{1}{98}$tự làm tiếp nha ( giống câu a)