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\(P=\frac{5}{2}+\frac{4}{11}+\frac{3}{22}+\frac{1}{30}+\frac{13}{60}=\left(\frac{4}{11}+\frac{3}{22}\right)+\left(\frac{5}{2}+\frac{1}{30}+\frac{13}{60}\right)=\frac{1}{2}+\frac{11}{4}=\frac{13}{4}\)
\(Q=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{19}{20}=\frac{1.2.3....19}{2.3.4....20}=\frac{1}{20}\)
\(A=\frac{1}{2.2}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\)
\(A=\frac{1}{4}+\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)\)
\(A=\frac{1}{4}+\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)
( gạch bỏ các phân số giống nhau)
\(A=\frac{1}{4}+\left(\frac{1}{3}-\frac{1}{9}\right)\)
\(A=\frac{1}{4}+\frac{2}{9}\)
\(A=\frac{17}{36}\)
phần b, c bn lm tương tự như phần a nha
Trả lời
a)
\(x^2:\frac{16}{11}=\frac{11}{4}\)
\(\Leftrightarrow x^2=\frac{11}{4}\cdot\frac{16}{11}\)
\(\Leftrightarrow x^2=\frac{16}{4}\)
\(\Leftrightarrow x^2=\left(\frac{4}{2}\right)^2\)
\(\Leftrightarrow x=\frac{4}{2}\)
Vậy x=\(\frac{4}{2}\)
b) (bạn thiếu nhóm \(\frac{1}{10\cdot13}\))
Đặt \(A=\frac{1}{1\cdot4}+\frac{1}{4\cdot7}+\frac{1}{7\cdot10}+\frac{1}{10\cdot13}+\frac{1}{13\cdot16}+\frac{1}{16\cdot19}\)
\(\Rightarrow3A=3\left(\frac{1}{1\cdot4}+\frac{1}{4\cdot7}+\frac{1}{7\cdot10}+\frac{1}{10\cdot13}+\frac{1}{13\cdot16}+\frac{1}{16\cdot19}\right)\)
\(\Rightarrow3A=\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+\frac{3}{10\cdot13}+\frac{3}{13\cdot16}+\frac{3}{16\cdot19}\)
\(\Rightarrow3A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}+\frac{1}{16}-\frac{1}{19}+\frac{1}{19}\)
\(\Rightarrow3A=1-\frac{1}{19}\Leftrightarrow3A=\frac{18}{19}\)
\(\Rightarrow A=\frac{18}{19}:3\Leftrightarrow A=\frac{6}{19}\)
a = \(\frac{13}{4}\)- \(\frac{9}{5}\)= \(\frac{29}{20}\)
30 % của 29/20 là : \(\frac{29}{20}\)x 30% = \(\frac{87}{200}\)