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1/15.18 + 1/18.21 + 1/21.24 + ... + 1/87.90
= 1/3.(3/15.18 + 3/18.21 + 3/21.24 + ... + 3/87.90)
= 1/3.(1/15 - 1/18 + 1/18 - 1/21 + 1/21 - 1/24 + ... + 1/97 - 1/90)
= 1/3.(1/15 - 1/90)
= 1/3.1/18
= 1/54
Đặt tổng trên là A
3A = \(\frac{1\cdot3}{15\cdot18}+\frac{1\cdot3}{18\cdot21}+...+\frac{1\cdot3}{87\cdot90}\)
\(=\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\)
\(=\frac{1}{15}-\frac{1}{90}\)
\(=\frac{1}{30}\)
\(A=\frac{1}{30}\div3=\frac{1}{30\cdot3}=\frac{1}{90}\)
\(#Louis\)
\(\dfrac{7}{21}+\dfrac{-9}{36}=\dfrac{1}{3}+\dfrac{-1}{4}=\dfrac{4}{12}+\dfrac{-3}{12}=\dfrac{1}{12}\)
\(\dfrac{-12}{18}+\dfrac{-21}{35}=\dfrac{-2}{3}+\dfrac{-3}{5}=\dfrac{-10}{15}+\dfrac{-9}{15}=\dfrac{-19}{15}\)
\(\dfrac{-18}{14}+\dfrac{15}{-21}=\dfrac{-9}{7}+\dfrac{-5}{7}=\dfrac{-14}{7}=-2\)
\(\dfrac{3}{21}+\dfrac{-6}{42}=\dfrac{1}{7}+\dfrac{-1}{7}=0\)
\(D=\frac{6}{15\times18}+\frac{6}{18\times21}+\frac{6}{21\times24}+...+\frac{6}{87\times90}\)
\(=2\times\left(\frac{3}{15\times18}+\frac{3}{18\times21}+...+\frac{3}{87\times90}\right)\)
\(=2\times\left(\frac{18-15}{15\times18}+\frac{21-18}{18\times21}+...+\frac{90-87}{87\times90}\right)\)
\(=2\times\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)
\(=2\times\left(\frac{1}{15}-\frac{1}{90}\right)=\frac{1}{9}\)
Ta có:
\(-\dfrac{18}{24}-\dfrac{15}{21}\) = \(-\left(\dfrac{18}{24}+\dfrac{15}{21}\right)\) = \(-\left(\dfrac{3}{4}+\dfrac{5}{7}\right)\) = \(-\dfrac{21+20}{28}\) = \(-\dfrac{41}{28}\)
\(s=\frac{6}{15\times18}+\frac{6}{18\times21}+\frac{6}{21\times24}+....+\frac{6}{87\times90}\)
\(s-3=\frac{3}{15\times18}+\frac{3}{18\times21}+\frac{3}{21\times24}+....+\frac{3}{87\times90}\)
\(s-3=\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+....+\frac{1}{87}-\frac{1}{90}\)
\(s-3=\frac{1}{15}-\frac{1}{90}\)
\(s-3=\frac{1}{18}\)
\(s=\frac{1}{18}+3\)
\(s=\frac{55}{18}\)
\(\dfrac{-18}{24}+\dfrac{15}{-21}=\dfrac{-3}{4}+\dfrac{-5}{7}=\dfrac{-21}{28}+\dfrac{-20}{28}=\dfrac{-41}{28}\)
\(\dfrac{-18}{24}+\dfrac{15}{-21}=\dfrac{-3}{4}+\dfrac{-5}{7}=\dfrac{-21}{28}+\dfrac{-20}{28}=\dfrac{-21+\left(-20\right)}{28}=\dfrac{-41}{28}\)
a) (-10)-21-18=-(10+21+18)=-49
b) 24-(-16)+(-15)=24+16-15=40-15=25
c) 49-[15+(-6)]=49-9=40
d) (-44)-[(-14)-30]=-44-(-44)=0
\(\frac{-18}{24}-\frac{15}{21}\)
\(=\frac{-3}{4}-\frac{5}{7}\)
\(=\frac{-21}{28}-\frac{20}{28}\)
\(=\frac{-41}{28}\)
-41/28