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\(\frac{74\times158+69}{158\times75-89}\)
= \(\frac{74\times158+69}{158\times\left(74+1\right)-89}\)
= \(\frac{74\times158+69}{158\times74+158-89}\)
= \(\frac{74\times158+69}{158\times74+\left(158-89\right)}\)
= \(\frac{74\times158+69}{74\times158+69}\)
= 1
\(A=\)\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}\)
\(A=\)\(1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+1-\frac{1}{30}+1-\frac{1}{42}+1-\frac{1}{56}+1-\frac{1}{72}+1-\frac{1}{90}\)
\(A=\)\(9-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)
\(A=\)\(9-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)
\(A=\)\(9-\left(1-\frac{1}{10}\right)\)
\(A=\)\(9-\frac{9}{10}\)
\(A=\)\(\frac{81}{10}\)
A=(1-1/2)+(1-1/6)+...+(1-89/90)
A=1x9-(1/2+1/6+...+1/90)
A=9-(1/1x2+1/2x3+...+1/9x10)
A=9-(1-1/2+1/2-1/3+1/3+...+1/9 -1/10)
A=9-(1-1/10)
A=9-9/10
A=81/10=8,1
hok tốt nhé
\(\left(-1-\frac{1}{12}\right).\left(-1-\frac{1}{13}\right).\left(-1-\frac{1}{14}\right)...\left(-1-\frac{1}{2017}\right)\)
\(=\frac{-13}{12}.\frac{-14}{13}.\frac{-15}{14}...\frac{-2018}{2017}\)
\(=\frac{-13}{12}.\frac{14}{-13}.\frac{-15}{14}...\frac{2018}{-2017}\)
\(=\frac{\left(-13\right).14.\left(-15\right)...2018}{12.\left(-13\right).14...2017}=\frac{2018}{12}=\frac{1009}{6}\)
\(\frac{4-\frac{3}{69}-\frac{168}{117}-\frac{75}{141}}{\frac{5}{69}+\frac{5}{117}+\frac{5}{141}}\)
=\(\frac{\frac{66}{69}-\frac{66}{117}-\frac{66}{141}}{\frac{5}{69}+\frac{5}{117}+\frac{5}{141}}\)
=\(\frac{66\left(\frac{1}{69}+\frac{1}{117}+\frac{1}{141}\right)}{5\left(\frac{1}{69}+\frac{1}{117}+\frac{1}{141}\right)}\)
=\(\frac{66}{5}\)
\(\frac{-3}{5}.\left(\frac{5}{7}+\frac{3}{7}+\frac{6}{7}\right)\)
=\(\frac{-3}{5}.\)\(\frac{14}{7}\)
=\(-\frac{3}{5}.2\)
=-6/5
M=3.(\(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-....+\frac{1}{59}-\frac{1}{60}\)\(\frac{1}{61}\))
M= 3.(\(\frac{1}{5}-\frac{1}{61}\))
M=\(\frac{168}{305}\)
\(M=\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{59.61}\)
\(M=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\right)\)
\(M=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)\)
\(M=\frac{84}{305}\)
\(=-\frac{3}{4}\left(5\frac{3}{13}+\frac{36}{13}\right)\)
\(=-\frac{3}{4}.\left(5+3\right)\)
\(=-\frac{3}{4}.8\)
\(=-6\)
\(\frac{74\times158+69}{158\times75-89}\)
= \(\frac{74\times158+69}{158\times\left(74+1\right)-89}\)
= \(\frac{74\times158+69}{158\times74+158-89}\)
= \(\frac{74\times158+69}{158\times74+\left(158-89\right)}\)
= \(\frac{74\times158+69}{74\times158+69}\)
= 1