Đáp án:
$1)
A=1\\
2)B=\dfrac{-5}{11}\\
3)
C=\dfrac{19}{23}\\
4)
F=
G=\dfrac{5}{39}\\
6)
H=\dfrac{12}{19}$
Giải thích các bước giải:
$1)
A=1\dfrac{1}{7}-\dfrac{1}{7}.\dfrac{2}{7}-\dfrac{1}{7}.\dfrac{5}{7}\\
=\dfrac{8}{7}-\dfrac{1}{7}.\dfrac{2}{7}-\dfrac{1}{7}.\dfrac{5}{7}\\
=\dfrac{1}{7}.\left ( 8-\dfrac{2}{7}-\dfrac{5}{7} \right )\\
=\dfrac{1}{7}.\left ( 8-\dfrac{7}{7} \right )\\
=\dfrac{1}{7}.7=1\\
2)B=\dfrac{5}{7}.\dfrac{5}{11}+\dfrac{5}{7}.\dfrac{2}{11}-\dfrac{5}{7}.\dfrac{14}{11}\\
=\dfrac{5}{7.11}.\left ( 5+2-14 \right )\\
=\dfrac{5}{7.11}.(-7)\\
=\dfrac{-5}{11}\\
3)
C=\dfrac{8}{3}.\dfrac{2}{5}.\dfrac{3}{8}.10.\dfrac{19}{92}\\
=\dfrac{8}{3}.\dfrac{3}{8}.\dfrac{2}{5}.10.\dfrac{19}{92}\\
=4.\dfrac{19}{92}=\dfrac{19}{23}\\
4)
F=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{19.20}\\
=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{19}-\dfrac{1}{20}\\
=\dfrac{1}{2}-\dfrac{1}{20}\\
=\dfrac{10}{20}-\dfrac{1}{20}\\
=\dfrac{9}{20}\\
5)
G=\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}\\
=\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}+\dfrac{1}{11.13}\\
=\dfrac{1}{2}.\left ( \dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}\right )\\
=\dfrac{1}{2}.\left ( \dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13} \right )\\
=\dfrac{1}{2}.\left ( \dfrac{1}{3}-\dfrac{1}{13} \right )\\
=\dfrac{1}{2}.\left ( \dfrac{13}{39}-\dfrac{3}{39} \right )\\
=\dfrac{1}{2}.\dfrac{10}{39}\\
=\dfrac{5}{39}\\
6)
H=\dfrac{1}{2}+\dfrac{1}{14}+\dfrac{1}{35}+\dfrac{1}{65}+\dfrac{1}{104}+\dfrac{1}{152}\\
=\dfrac{2}{4}+\dfrac{2}{28}+\dfrac{2}{70}+\dfrac{2}{130}+\dfrac{2}{208}+\dfrac{2}{304}\\
=\dfrac{2}{3}.\left ( \dfrac{3}{4}+\dfrac{3}{28}+\dfrac{3}{70}+\dfrac{3}{130}+\dfrac{3}{208}+\dfrac{3}{304} \right )\\
=\dfrac{2}{3}.\left ( \dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+\dfrac{3}{13.16}+\dfrac{3}{16.19} \right )\\
=\dfrac{2}{3}.\left ( \dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{19} \right )\\
=\dfrac{2}{3}.\left ( 1-\dfrac{1}{19} \right )\\
=\dfrac{2}{3}.\dfrac{18}{19}\\
=\dfrac{12}{19}$
