Đăt :
\(A=\dfrac{2}{1.4}+\dfrac{2}{4.7}+.........+\dfrac{2}{49.51}\)
\(\dfrac{3}{2}A=\dfrac{3}{1.4}+\dfrac{3}{4.7}+..........+\dfrac{3}{49.51}\)
\(\dfrac{3}{2}A=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+.........+\dfrac{1}{49}-\dfrac{1}{51}\)
\(\dfrac{3}{2}A=1-\dfrac{1}{51}\)
\(\dfrac{3}{2}A=\dfrac{50}{51}\)
\(\Rightarrow A=\dfrac{50}{51}:\dfrac{3}{2}=\dfrac{100}{153}\)
Ta có công thức nha sau :
\(\dfrac{a}{b.c}=\dfrac{a}{c-b}.\left(\dfrac{1}{b}-\dfrac{1}{c}\right)\)
Ta gọi biểu thức phân số là A
Vậy \(\dfrac{2}{1.4}=\dfrac{2}{4-1}.\left(1-\dfrac{1}{4}\right)\)
\(\dfrac{2}{4.7}=\dfrac{2}{7-4}.\left(\dfrac{1}{4}-\dfrac{1}{7}\right)\)
\(\dfrac{2}{7.10}=\dfrac{2}{10-7}.\left(\dfrac{1}{7}-\dfrac{1}{10}\right)\)
Ta thấy 50 - 49 = 1 , không bằng những biểu thức kia bằng 3 nên ta tách những biểu thức đó ra.
A= \(\dfrac{2}{3}.\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}\right)+\dfrac{2}{49.50}\)
\(A=\dfrac{2}{3}.\left(1-\dfrac{1}{10}\right)+2.\left(\dfrac{1}{49}-\dfrac{1}{50}\right)\)
\(A=\dfrac{18}{30}+\left(\dfrac{1}{1225}\right)=\dfrac{736}{1225}\)
mink chắc chắn, ủng hộ nha
\(\dfrac{2}{1.4}+\dfrac{2}{4.7}+\dfrac{2}{7.10}+\dfrac{2}{49.50}\)
\(=\dfrac{2}{3}\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}\right)+\left(2.\dfrac{1}{49.50}\right)\)
\(=\dfrac{2}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}\right)+2\left(\dfrac{1}{49}-\dfrac{1}{50}\right)\)
\(=\dfrac{2}{3}\left(1-\dfrac{1}{10}\right)+2\left(\dfrac{50}{2450}-\dfrac{49}{2450}\right)\)
\(=\dfrac{2}{3}.\dfrac{9}{10}+2.\dfrac{1}{2450}\)
\(=\dfrac{3}{5}+\dfrac{1}{1225}\)
\(=\dfrac{735}{1225}+\dfrac{1}{1225}\)
\(=\dfrac{736}{1225}\)
