\(\dfrac{6}{3\cdot5}+\dfrac{6}{5\cdot7}+\dfrac{6}{7\cdot9}+...+\dfrac{6}{55\cdot57}\)
\(=3\left(\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+...+\dfrac{2}{55\cdot57}\right)\)
\(=3\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{55}-\dfrac{1}{57}\right)\)
\(=3\left(\dfrac{1}{3}-\dfrac{1}{57}\right)=3\cdot\dfrac{6}{19}=\dfrac{18}{19}\)
\(\dfrac{6}{3\cdot5}+\dfrac{6}{5\cdot7}+\dfrac{6}{7\cdot9}+...+\dfrac{6}{55\cdot57}\\ =3\left(\dfrac{1}{3\cdot5}+\dfrac{1}{5\cdot7}+\dfrac{1}{7\cdot9}+...+\dfrac{1}{55\cdot57}\right)\\ =3\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{55}-\dfrac{1}{57}\right)\\ =3\left(\dfrac{1}{3}-\dfrac{1}{57}\right)\\ =3\cdot\dfrac{6}{19}\\ =\dfrac{18}{19}\)
Viết theo cách ps Ai Cập ấy bạn :
= 6 (1/3.5 + 1/5.7 + .... + 1/55.57)
= 6(1/3 - 1/5 + 1/5 - 1/7 + .... + 1/55 - 1/57)
= 6( 1/3 - 1/57)
= 6 . 6/19
=36/19
chúc bạn giải đc ^^
lộn ^^
mình quên ^^
làm theo cách bạn Ace Legona ấy ^^
mình làm lộn , lấy 3 làm mẫu chung ^^
