Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\Rightarrow A=\frac{14}{15}.\frac{20}{21}.\frac{41}{42}.....\frac{209}{210}\)
\(=\frac{4.7}{5.6}.\frac{5.8}{6.7}.\frac{6.9}{7.8}.....\frac{19.22}{20.21}\)
\(=\frac{22}{6}=\frac{11}{3}\)
ta có
1/2 P=1/2(1-1/10-1/15-1/3-1/28-1/6-1/21)
=1/2-(1/6+1/12+1/20+1/30+1/42+1/56)
=1/2-(1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8)
=1/2-(1/2-1/8)
=1/8
suy ra P=1/4
ta có
1/2 P=1/2(1-1/10-1/15-1/3-1/28-1/6-1/21)
=1/2-(1/6+1/12+1/20+1/30+1/42+1/56)
=1/2-(1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8)
=1/2-(1/2-1/8)
=1/8
suy ra P=1/4
`Answer:`
\(C=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{210}\right)\)
\(=\left(\frac{3}{3}-\frac{1}{3}\right)\left(\frac{6}{6}-\frac{1}{6}\right)\left(\frac{10}{10}-\frac{1}{10}\right)\left(\frac{15}{15}-\frac{1}{15}\right)...\left(\frac{210}{210}-\frac{1}{210}\right)\)
\(=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{209}{210}\)
\(=\frac{2.2}{3.2}.\frac{5.2}{6.2}.\frac{9.2}{10.2}...\frac{209.2}{210.2}\)
\(=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}...\frac{418}{420}\)
\(=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{19.22}{20.21}\)
\(=\frac{1.4.2.5.3.6...19.22}{2.3.3.4.4.5...20.21}\)
\(=\frac{\left(1.2.3...19\right)\left(4.5.6...22\right)}{\left(2.3.4...20\right)\left(3.4.5...21\right)}\)
\(=\frac{11}{30}\)
\(A=-5,13:\left(5\dfrac{5}{28}-1\dfrac{8}{9}.1,25+1\dfrac{16}{63}\right)\)
\(=-5,13:\left(5\dfrac{5}{28}-2\dfrac{13}{36}+1\dfrac{16}{63}\right)\)
\(=5,13:\left[\left(5-2+1\right)+\left(\dfrac{5}{28}-\dfrac{13}{36}+\dfrac{16}{63}\right)\right]\)
\(=5,13:\left(4+\dfrac{1}{14}\right)\)
\(=1,26\)
\(\frac{-1}{21}+\frac{-1}{28}=\frac{-4}{84}+\frac{-3}{84}=\frac{-7}{84}=\frac{-1}{12}\)