B = \(\dfrac{1}{1}.2+\dfrac{1}{2}.3+..........+\dfrac{1}{9}.10\) Lên lớp 6 dấu chấm là dấu nhân
B = \(\dfrac{2}{1}+\dfrac{3}{2}+\dfrac{4}{3}+\dfrac{5}{4}+\dfrac{6}{5}+\dfrac{7}{6}+\dfrac{8}{7}+\dfrac{9}{8}+\dfrac{10}{9}\)
B = \(\dfrac{1+1}{1}\) + \(\dfrac{2+1}{2}+\dfrac{4+1}{4}+\dfrac{5+1}{5}+\dfrac{6+1}{6}+\dfrac{7+1}{7}+\dfrac{8+1}{8}+\dfrac{9+1}{9}\)
B = \(\dfrac{1}{1}+\dfrac{1}{1}-\dfrac{2}{2}+\dfrac{1}{2}-\dfrac{3}{3}+\dfrac{1}{3}-\dfrac{4}{4}+\dfrac{1}{4}-\dfrac{5}{5}+\dfrac{1}{5}-\dfrac{6}{6}+\dfrac{1}{6}-\dfrac{7}{7}+\dfrac{1}{7}-\dfrac{8}{8}+\dfrac{1}{8}+\dfrac{9}{9}+\dfrac{1}{9}\)
B = 10 + ( \(\dfrac{1}{1.2}+\dfrac{1}{1.3}+\dfrac{1}{2.4}+\dfrac{1}{1.5}+\dfrac{1}{2.3}+\dfrac{1}{1.7}+\dfrac{1}{2.4}+\dfrac{1}{1.9}\) )
B = 10 + ( \(\dfrac{1}{1}.\dfrac{1}{2}+\dfrac{1}{1}.\dfrac{1}{3}+\dfrac{1}{2}.\dfrac{1}{4}+\dfrac{1}{1}.\dfrac{1}{5}+\dfrac{1}{2}.\dfrac{1}{3}+\dfrac{1}{1}.\dfrac{1}{7}+\dfrac{1}{2}.\dfrac{1}{4}+\dfrac{1}{1}.\dfrac{1}{9}\) )
B = 10 + ( \(\dfrac{1}{5}+\dfrac{1}{7}+\dfrac{1}{9}\) )
B = 10 + 143/315
B = \(\dfrac{3613}{3150}\)
mik nghĩ là mình sai bạn à
Ta có: \(B=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{9\cdot10}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=1-\dfrac{1}{10}\)
\(=\dfrac{9}{10}\)
