Jup e nhé
c)
Ta có :
\(\dfrac{1}{5}+\dfrac{1}{35}+\dfrac{1}{63}+...+\dfrac{1}{143}\)
\(=\dfrac{1}{5}+\dfrac{1}{5}.\dfrac{1}{7}+\dfrac{1}{7}.\dfrac{1}{9}+....+\dfrac{1}{11}.\dfrac{1}{13}\)
\(=\dfrac{1}{2}.\left(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+....+\dfrac{1}{11}-\dfrac{1}{13}\right)\)
\(=\dfrac{1}{2}.\left(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{1}{13}\right)=\dfrac{1}{2}.\dfrac{29}{130}=\dfrac{29}{260}\)
Chúc bạn học tốt =))
d)Tính \(\dfrac{10}{3}+\dfrac{1}{6}\) và \(\dfrac{25}{2}-\dfrac{1}{4}\)
c)\(\dfrac{1}{1\cdot5}+\dfrac{1}{5\cdot7}+...+\dfrac{1}{11\cdot13}\)
Ok tự lm nốt e nhé ! v~
Cho mình sửa lại một chút nha , làm nhầm
\(C=\dfrac{1}{5}+\dfrac{1}{35}+\dfrac{1}{63}+...+\dfrac{1}{143}\)
\(=\dfrac{1}{5}+\dfrac{1}{5}.\dfrac{1}{7}+\dfrac{1}{7}.\dfrac{1}{9}+....+\dfrac{1}{11}.\dfrac{1}{13}\)
\(=\dfrac{1}{5}+\dfrac{1}{2}\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{11}-\dfrac{1}{13}\right)\)
\(=\dfrac{1}{5}+\dfrac{1}{2}.\left(\dfrac{1}{5}-\dfrac{1}{13}\right)=\dfrac{1}{5}+\dfrac{1}{2}.\left(\dfrac{8}{65}\right)\)
\(=\dfrac{1}{5}+\dfrac{4}{65}\)
\(=\dfrac{17}{65}\)
Vậy C = 17/65
Chúc bn hok tốt
