Đáp án:
Giải thích các bước giải:
$4A.$
$a,A=\dfrac{1}{6} ; B=\dfrac{1}{12} ; C=\dfrac{1}{20}$
$b,A+B=\dfrac{1}{6}+\dfrac{1}{12}=\dfrac{3}{4}$
$A+B+C=\dfrac{3}{4}+\dfrac{1}{20}=\dfrac{4}{5}$
$c,D=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+....+\dfrac{1}{19.20}$
$=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}....+\dfrac{1}{19}-\dfrac{1}{20}$
$=\dfrac{1}{2}-\dfrac{1}{20}=\dfrac{9}{20}$
$E=\dfrac{1}{99}-\dfrac{1}{99.98}-\dfrac{1}{98.97}-...-\dfrac{1}{2.1}$
$E=\dfrac{1}{99}-\left (\dfrac{1}{1}-\dfrac{1}{2} +\dfrac{1}{2}-\dfrac{1}{3} +\dfrac{1}{3}-...\dfrac{1}{99} \right )$
$E=\dfrac{1}{99}-\dfrac{98}{99}$
$E=\dfrac{-97}{99}$
$4B.$
$a,M=\dfrac{2}{3} ; N=\dfrac{2}{15} ; P=\dfrac{2}{35}$
$b,M+N=\dfrac{2}{3}+\dfrac{2}{15}=\dfrac{4}{5}$
$M+N+P=\dfrac{4}{5}+\dfrac{2}{35}=\dfrac{5}{6}$
$c,E=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{19.21}$
$=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-...+\dfrac{1}{19}-\dfrac{1}{21}$
$=1-\dfrac{1}{21}$
$=\dfrac{20}{21}$
$F=\dfrac{1}{99}-\dfrac{1}{99.97}-\dfrac{1}{97.95}-...-\dfrac{1}{3.1}$
$F=\dfrac{1}{99}-\dfrac{1}{2}.\left (\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-....-\dfrac{1}{99} \right )$
$F=\dfrac{1}{99}-\dfrac{1}{2}.\dfrac{98}{99}$
$F=\dfrac{1}{99}-\dfrac{49}{99}$
$=\dfrac{-16}{33}$
