Bài 1 :

a) \(A=\frac{-1}{4.5}+\frac{-1}{5.6}-\frac{-1}{7.8}+\frac{-1}{9.10}\)

\(A=\frac{1}{4}\)\(-\left(-\frac{1}{5}\right)+...+\left(-\frac{1}{9}\right)-\left(-\frac{1}{10}\right)\)

\(A=\frac{1}{4}+\frac{1}{10}\)

\(A=\frac{3}{20}\)

Bài 2:

a,17178585=1717:17178585:1717=15;13135151=1313:1015151:101=135115=51255<65255=1351⇒17178585<13135151a,17178585=1717:17178585:1717=15;13135151=1313:1015151:101=135115=51255<65255=1351⇒17178585<13135151

b,201201202202=201201:1001202202:1001=201202=201⋅1001001202⋅1001001=201201201202202202

A= \(\frac{-1}{4\cdot5}+\frac{-1}{5\cdot6}+\frac{-1}{6\cdot7}+\frac{-1}{7\cdot8}+\frac{-1}{8\cdot9}+\frac{-1}{9\cdot10}\)

=\(-1\left(\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\right)\)

=\(-1\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}\right)\)

=\(-1\left(\frac{1}{4}-\frac{1}{10}\right)\)

=\(-1\cdot\frac{3}{20}\)

=\(\frac{-3}{20}\)

=\(\frac{-1}{20}\)

phân tích mẫu: 20=4.5 , 30= 5.6 , 42=6.7 tương tự rồi tách cả phân số là được

\(A=-\frac{1}{20}+-\frac{1}{30}+-\frac{1}{42}+-\frac{1}{56}+-\frac{1}{72}+-\frac{1}{90}\)

\(\Rightarrow A=-1\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{9.10}\right)\)

\(A=-1\left(\frac{1}{4}-\frac{1}{10}\right)\)

\(\Rightarrow A=-\frac{3}{20}\)

\(A=\frac{-1}{20}-\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)

\(A=-\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)

\(A=-\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(A=-\left(\frac{1}{4}-\frac{1}{10}\right)\)

\(A=\frac{-3}{20}\)

#

A=\(\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)\(\frac{-1}{90}\)

A=\(-1-\left(\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\right)\)

A=\(-1-\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)

A=\(-1-\left(\frac{1}{4}-\frac{1}{10}\right)\)

A=\(-1-\frac{3}{20}\)

A=\(-1\frac{3}{20}\)

\(a,A=\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)

\(=\frac{-1}{4.5}+\frac{-1}{5.6}+\frac{-1}{6.7}+\frac{-1}{7.8}+\frac{-1}{8.9}+\frac{-1}{9.10}\)

\(=\frac{-1}{4}+\frac{1}{5}-\frac{1}{5}+\frac{1}{6}-...-\frac{1}{9}+\frac{1}{10}\)

\(=-\frac{1}{4}+\frac{1}{10}\)

\(=-\frac{3}{20}\)

\(b,B=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)

\(\frac{B}{7}=\frac{5}{2.7}+\frac{4}{11.7}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)

\(=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-....-\frac{1}{28}\)

\(=\frac{1}{2}-\frac{1}{28}=\frac{13}{28}\)

a) \(A=\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)

\(\Rightarrow-1.A=\frac{1}{20}+\frac{1}{30}+........+\frac{1}{90}\)

\(=\frac{1}{4.5}+\frac{1}{5.6}+........+\frac{1}{9.10}\)

\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+........+\frac{1}{9}-\frac{1}{10}=\frac{1}{4}-\frac{1}{10}=\frac{3}{20}\)

\(\Rightarrow A=\frac{3}{20}:\left(-1\right)=\frac{-3}{20}\)

b) \(B=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)

\(\Rightarrow\frac{1}{7}B=\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\)

\(=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\)

\(=\frac{1}{2}-\frac{1}{28}=\frac{13}{28}\)

\(\Rightarrow B=\frac{13}{28}:\frac{1}{7}=\frac{13}{28}.7=\frac{13}{4}\)

                                                                  Bài giải

a, \(A=\frac{-1}{20}+\frac{-1}{30}+\frac{-1}{42}+\frac{-1}{56}+\frac{-1}{72}+\frac{-1}{90}\)

\(-1A=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)

\(-1A=\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\)

\(-1A=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)

\(-1A=\frac{1}{4}-\frac{1}{10}\)

\(-1A=\frac{3}{20}\)

\(A=\frac{3}{20\text{ }}\text{ : }\left(-1\right)=-\frac{3}{20}\)

b, \(B=\frac{5}{2\cdot1}+\frac{4}{1\cdot11}+\frac{3}{11\cdot2}+\frac{1}{2\cdot15}+\frac{13}{15\cdot4}\)

\(\frac{1}{7}B=\frac{5}{2\cdot7}+\frac{4}{7\cdot11}+\frac{3}{11\cdot14}+\frac{1}{14\cdot15}+\frac{13}{15\cdot28}\)

\(\frac{1}{7}B=\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\)

\(\frac{1}{7}B=\frac{1}{2}-\frac{1}{28}\)

\(\frac{1}{7}B=\frac{13}{28}\)

\(B=\frac{13}{28}\text{ : }\frac{1}{7}=\frac{13}{4}\)

A = \(\frac{-79}{90}\)

B = \(\frac{8}{9}\)

cách giải sao chỉ mình với

Đè thừa một số \(\frac{25}{156}\),mk ko lại đề bài nhé

\(A=1-\frac{2+3}{2\cdot3}+.....+\frac{11+12}{11\cdot12}-\frac{12+13}{12\cdot13}\)

\(=1-\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+\frac{1}{4}-...+\frac{1}{11}+\frac{1}{12}-\frac{1}{12}-\frac{1}{13}\)

\(=\frac{1}{2}-\frac{1}{13}=\frac{11}{26}\)

Thanks "Blue Moon" nhìu nha

\(A=-\frac{1}{20}+-\frac{1}{30}+-\frac{1}{42}+...+-\frac{1}{90}\)

\(\Leftrightarrow A=\left(-1\right)\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(A=\left(-1\right)\left(\frac{1}{4}-\frac{1}{10}\right)\)

\(A=-\frac{3}{20}\)

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\)

\(=1-\frac{1}{10}=\frac{9}{10}\)

Bạn biết bài này rồi phải không =.="

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