giúp mình với
a) A=1/3.4-1/4.5-1/5.6-...-1/9.10
b)B=7/3.4-9/4.5+11/5.6-13/6.7+15/7.8-17/8.9
Ai làm được mình cho 1 like :))
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7/3.4 - 9/4.5 + 11/5.6 - 13/6.7 + 15/7.8 - 17/8.9 + 19/9.10
= 3+4/3.4 - 4+5/4.5 + 5+6/5.6 - 6+7/6.7 + 7+8/7.8 - 8+9/8.9 + 9+10/9.10
=1/3 + 1/4 - 1/4 - 1/5 + 1/5 + 1/6 -1/6 - 1/7 +1/7 +1/8 - 1/8 - 1/9 + 1/9 + 1/10
=1/3 + 1/10=13/30
\(=\frac{6+1}{12}-\frac{10-1}{20}+\frac{10+1}{30}-\frac{14-1}{42}+\frac{14+1}{56}-\frac{18-1}{72}+\frac{18+1}{90}\)
=\(\frac{6}{12}+\frac{1}{12}-\frac{10}{20}+\frac{1}{20}+\frac{10}{30}+\frac{1}{30}-\frac{14}{42}+\frac{1}{42}+\frac{14}{56}+\frac{1}{56}-\frac{18}{72}+\frac{1}{72}+\frac{18}{90}+\frac{1}{90}\)
=\(\frac{1}{2}+\frac{1}{12}-\frac{1}{2}+\frac{1}{20}+\frac{1}{3}+\frac{1}{30}-\frac{1}{3}+\frac{1}{42}+\frac{1}{4}+\frac{1}{56}-\frac{1}{4}+\frac{1}{72}+\frac{1}{5}+\frac{1}{90}\)
\(=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{5}\)
\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{6}\)
\(=\frac{1}{3}-\frac{1}{10}+\frac{1}{5}\)
\(=\frac{10}{30}-\frac{3}{30}+\frac{6}{30}=\frac{13}{30}\)
\(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
=\(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)
=\(\frac{1}{3}-\frac{1}{8}\)
=\(\frac{8}{24}-\frac{3}{24}\)
=\(\frac{5}{24}\)
A=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9
A=1/3-1/9
A=2/9
các câu 2;3 còn lại giống câu 1 bạn nhé
bạn thay số vào rồi làm tương tự
đặt \(M=\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}\)
ta có:
\(M=\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}\)
\(\Leftrightarrow M=\dfrac{3+4}{3.4}-\dfrac{4+5}{4.5}+\dfrac{5+6}{5.6}-\dfrac{6+7}{6.7}+\dfrac{7+8}{7.8}-\dfrac{8+9}{8.9}+\dfrac{9+10}{9.10}\) \(\Leftrightarrow M=\dfrac{3}{3.4}+\dfrac{4}{3.4}-\dfrac{4}{4.5}-\dfrac{5}{4.5}+\dfrac{5}{5.6}+\dfrac{6}{5.6}-\dfrac{6}{6.7}-\dfrac{7}{6.7}+\dfrac{7}{7.8}+\dfrac{8}{7.8}-\dfrac{8}{8.9}-\dfrac{9}{8.9}+\dfrac{9}{9.10}+\dfrac{10}{9.10}\) \(\Rightarrow M=\dfrac{1}{4}+\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{5}-\dfrac{1}{7}-\dfrac{1}{6}+\dfrac{1}{8}+\dfrac{1}{7}-\dfrac{1}{9}-\dfrac{1}{8}+\dfrac{1}{10}+\dfrac{1}{9}\) \(\Rightarrow M=\dfrac{1}{3}+\dfrac{1}{10}\)
\(\Rightarrow M=\dfrac{10}{30}+\dfrac{3}{30}\)
\(\Rightarrow M=\dfrac{13}{30}\)
vậy M = \(\dfrac{13}{30}\)
vậy \(\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}=\dfrac{13}{30}\)
\(\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}=\dfrac{3+4}{3.4}-\dfrac{4+5}{4.5}+\dfrac{5+6}{5.6}-\dfrac{6+7}{6.7}+\dfrac{7+8}{7.8}-\dfrac{8+9}{8.9}+\dfrac{9+10}{9.10}=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}=\dfrac{1}{3}-\dfrac{1}{10}=\dfrac{7}{30}\)