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\(D=\dfrac{2}{3}.\dfrac{5}{5.8}+\dfrac{11}{8.19}+\dfrac{13}{19.32}\)
\(=\dfrac{2.5}{3.(5.8)}+\dfrac{11}{8.19}+\dfrac{13}{19.32}\)
\(=\dfrac{10}{3.5.8}+\dfrac{11}{8.19}+\dfrac{13}{19.32}\)
\(=\dfrac{1}{3.4}+\dfrac{11}{8.19}+\dfrac{13}{19.32}\)
\(=\dfrac{17}{96}\)
\(A=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{9900}\)
\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{99\cdot100}\)
\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(A=1-\dfrac{1}{100}=\dfrac{99}{100}\)
\(B=\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+..+\dfrac{1}{195}\) ( là 195 ms đúng ! )
\(B=\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+\dfrac{1}{5\cdot7}+...+\dfrac{1}{13\cdot15}\)
\(B=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{13}-\dfrac{1}{15}\right)\)
\(B=\dfrac{1}{2}\left(1-\dfrac{1}{15}\right)=\dfrac{1}{2}\cdot\dfrac{14}{15}=\dfrac{7}{15}\)
\(C=\dfrac{1}{2\cdot4}+\dfrac{1}{4\cdot6}+\dfrac{1}{6\cdot8}+...+\dfrac{1}{98\cdot100}\)
Rồi làm tương tự cân b nha!
\(D=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{32}+\dfrac{1}{32}-\dfrac{1}{57}\)
\(+\dfrac{1}{57}-\dfrac{1}{87}\)
\(D=\dfrac{1}{3}-\dfrac{1}{87}=\dfrac{28}{87}\)
\(=\dfrac{4}{1\cdot5}-\left(\dfrac{3}{5\cdot8}+\dfrac{11}{8\cdot19}+\dfrac{12}{19\cdot31}+\dfrac{70}{31\cdot101}+\dfrac{99}{101\cdot200}\right)\)
\(=1-\dfrac{1}{5}-\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{31}+\dfrac{1}{31}-\dfrac{1}{101}+\dfrac{1}{101}-\dfrac{1}{200}\right)\)
\(=1-\dfrac{1}{5}-\dfrac{1}{5}+\dfrac{1}{200}\)
\(=\dfrac{201}{200}-\dfrac{2}{5}=\dfrac{201-80}{200}=\dfrac{121}{200}\)
\(A=\frac{2}{3.5}+\frac{3}{5.8}+\frac{11}{8.19}+\frac{13}{19.32}+\frac{25}{32.57}+\frac{30}{57.87}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{19}+\frac{1}{19}-\frac{1}{32}+\frac{1}{32}-\frac{1}{57}+\frac{1}{57}-\frac{1}{87}\)
\(=\frac{1}{3}-\frac{1}{87}=\frac{29}{87}-\frac{1}{87}=\frac{28}{87}\)
\(\frac{2}{3.5}+\frac{3}{5.8}+\frac{11}{8.19}+\frac{13}{19.32}+\frac{25}{32.57}+\frac{30}{57.87}\)
\(=\frac{5-3}{3.5}+\frac{8-5}{3}+\frac{19-8}{8.19}+\frac{32-29}{19.32}+\frac{57-32}{32.57}+\frac{87-57}{57.87}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{19}+\frac{1}{19}-\frac{1}{32}+\frac{1}{32}-\frac{1}{57}+\frac{1}{57}-\frac{1}{87}\)
\(=\frac{1}{3}-\frac{1}{87}=\frac{28}{87}\)
\(C=\dfrac{2}{3\cdot5}+\dfrac{3}{5\cdot8}+\dfrac{11}{8\cdot19}+\dfrac{13}{19\cdot32}+\dfrac{25}{32\cdot57}+\dfrac{30}{57\cdot87}\)\(C=\left(\dfrac{5-3}{3\cdot5}\right)+\left(\dfrac{8-5}{5\cdot8}\right)+\left(\dfrac{19-8}{8\cdot19}\right)+\left(\dfrac{32-19}{19\cdot32}\right)+\left(\dfrac{57-32}{32\cdot57}\right)+\left(\dfrac{87-57}{57\cdot87}\right)\)\(C=\left(\dfrac{1}{3}-\dfrac{1}{5}\right)+\left(\dfrac{1}{5}-\dfrac{1}{8}\right)+\left(\dfrac{1}{8}-\dfrac{1}{19}\right)+\left(\dfrac{1}{19}-\dfrac{1}{32}\right)+\left(\dfrac{1}{32}-\dfrac{1}{57}\right)+\left(\dfrac{1}{57}+\dfrac{1}{87}\right)\)\(C=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{32}+\dfrac{1}{32}-\dfrac{1}{57}+\dfrac{1}{57}-\dfrac{1}{87}\)\(C=\dfrac{1}{3}-\dfrac{1}{87}=\dfrac{28}{87}\)
\(S=\frac{2}{3.5}+\frac{3}{5.8}+\frac{11}{8.19}+\frac{13}{19.32}+\frac{25}{32.57}+\frac{30}{57.85}\)
\(S=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{19}+\frac{1}{19}-\frac{1}{32}+\frac{1}{32}-\frac{1}{57}+\frac{1}{57}-\frac{1}{87}\)
\(S=\frac{1}{3}-\frac{1}{87}\)
\(S=\frac{28}{87}\)
a: =-21/36-3/36=-24/36=-2/3
b: =43/12*1/2+5/24=43/24+5/24=2
c: =8/9+1/9=1
e: =1-1/4+1/4-1/7+...+1/97-1/100
=1-1/100=99/100
\(D=\dfrac{2}{3}.\dfrac{5}{5.8}+\dfrac{11}{8.19}+\dfrac{13}{19.32}\)
\(D=\dfrac{2.5}{2.5.8}+\dfrac{1}{19}.\dfrac{11}{8}+\dfrac{1}{19}.\dfrac{13}{32}\)
\(D=\dfrac{1}{12}+\dfrac{1}{19}.\left(\dfrac{11}{8}+\dfrac{13}{32}\right)\)
\(D=\dfrac{1}{12}+\dfrac{1}{19}.\left(\dfrac{44}{32}+\dfrac{13}{32}\right)\)
\(D=\dfrac{1}{12}+\dfrac{1}{19}.\dfrac{57}{32}\)
\(D=\dfrac{1}{12}+\dfrac{3}{32}\)
\(D=\dfrac{8}{96}+\dfrac{9}{96}\)
\(D=\dfrac{17}{96}\)