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\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
\(=\frac{1}{3}-\frac{1}{21}\)
\(=\frac{7}{21}-\frac{1}{21}=\frac{6}{21}\)
\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)
\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
\(A=\frac{1}{3}+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)+\left(\frac{1}{9}-\frac{1}{9}\right)+...+\left(\frac{1}{19}-\frac{1}{19}\right)-\frac{1}{21}\)
\(A=\frac{1}{3}-\frac{1}{21}\)
\(A=\frac{2}{7}\)
\(=1+\frac{1}{3}+1+\frac{1}{15}+...+1+\frac{1}{399}.\)
\(=10+\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{19.21}\)
=\(10+\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{21}\right)\)
=\(10+\frac{1}{2}\left(1-\frac{1}{21}\right)=10+\frac{1}{2}.\frac{20}{21}=\frac{220}{21}\)
Ta có:
\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}.\frac{48}{49}=\frac{1.3}{2.2}+\frac{2.4}{3.3}+\frac{3.5}{4.4}+\frac{4.6}{5.5}+\frac{5.7}{6.6}+\frac{6.8}{7.7}=\frac{1.2.3.4.5.6}{2.3.4.5.6.7}.\frac{3.4.5.6.7.8}{2.3.4.5.6.7}=\frac{1}{7}.\frac{8}{2}=\frac{4}{7}\)
mình biết đáp án là : \(\frac{9}{16}\)thôi,còn cách giải thì mình không chắc chắn nên không viết ra
\(\frac{3.2.4.3.5.4.6.5.7.6.8.7.9}{4.3.3.4.4.5.5.6.6.7.7.8.8}\)= \(\frac{9}{16}\)
=\(\frac{3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\frac{3\cdot5}{4\cdot4}\cdot...\cdot\frac{49\cdot51}{50\cdot50}\)
=\(\frac{\left(2\cdot3\cdot...\cdot49\right)\cdot\left(3\cdot4\cdot...\cdot51\right)}{\left(2\cdot3\cdot4\cdot...\cdot50\right)\left(2\cdot3\cdot4\cdot...\cdot50\right)}\)
=\(\frac{51}{50\cdot2}=\frac{51}{100}\)
\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{2499}{2500}=\frac{3.8.15.2499}{4.9.16.2500}\)\(=\frac{14994}{24000}\)
(Thực hiện rút gọn)
# Học tốt #
\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{2499}{2500}=\frac{3.8.15.2499}{4.9.16.2500}=\frac{3.15.2499}{4.9.2.2500}\)
Tự rút gọn tiếp đi