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\(x\)là dấu nhân hả bạn? Nếu vậy thì mk làm cho nhé
\(A=\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot....\cdot\left(1-\frac{1}{20}\right)\)
\(A=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot.......\cdot\frac{17}{18}\cdot\frac{18}{19}\cdot\frac{19}{20}=\frac{1}{20}\)
Vậy \(A=\frac{1}{20}\)
\(B=1\frac{1}{2}\cdot1\frac{1}{3}\cdot1\frac{1}{4}\cdot........\cdot1\frac{1}{2005}\cdot1\frac{1}{2006}\cdot1\frac{1}{2007}\)
\(B=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot......\cdot\frac{2006}{2005}\cdot\frac{2007}{2006}\cdot\frac{2008}{2007}=\frac{2008}{2}=1004\)
Vậy \(B=1004\)
DẤU CHẤM LÀ DẤU NHÂN
a,
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{19}{20}=\frac{1}{20}\)
b, \(1\frac{1}{2}.1\frac{1}{3}....1\frac{1}{2017}=\frac{3}{2}.\frac{4}{3}....\frac{2018}{2017}=\frac{2018}{2}=1009\)
\(M=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\frac{1}{1+2+3+4+5}\)
\(M=\frac{1}{\left(1+2\right).2:2}+\frac{1}{\left(1+3\right).3:2}+\frac{1}{\left(1+4\right).4:2}+\frac{1}{\left(1+5\right).5:2}\)
\(M=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}\)
\(M=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)
\(M=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)
\(M=2.\left(\frac{1}{2}-\frac{1}{6}\right)\)
\(M=2.\frac{1}{2}-2.\frac{1}{6}\)
\(M=1-\frac{1}{3}=\frac{2}{3}\)
\(1\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}......1\frac{1}{1963}\)
\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}....\frac{1964}{1963}\)
\(=\frac{3.4.5....1964}{2.3.4....1963}\)
\(=\frac{1964}{2}=982\)
\(1\frac{1}{2}\)x\(1\frac{1}{3}\)x\(1\frac{1}{4}\)x.....x\(1\frac{1}{1963}\)
=\(\frac{3}{2}\)x\(\frac{4}{3}\)x\(\frac{5}{4}\)x.....x\(\frac{1964}{1963}\)
=\(1964:2\frac{1}{1}\)
=983
\(1\frac{1}{2}x1\frac{1}{3}:1\frac{1}{4}:1\frac{1}{5}\)
\(=\frac{3}{2}x\frac{4}{3}:\frac{5}{4}:\frac{6}{5}\)
\(=\frac{3}{2}x\frac{4}{3}x\frac{4}{5}x\frac{5}{6}\)
\(=\frac{4x4}{2x6}=\frac{2x2x4}{2x2x3}=\frac{4}{3}\)
\(1\frac{1}{2}\times1\frac{1}{3}\div1\frac{1}{4}\div1\frac{1}{5}=\frac{3}{2}\times\frac{4}{3}\div\frac{5}{4}\div\frac{6}{5}=\frac{3}{2}\times\frac{4}{3}\times\frac{4}{5}\times\frac{5}{6}\)
\(=\frac{3\times4\times4\times5}{2\times3\times5\times6}=\frac{4}{3}\)
\(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{5}\right)x\left(1-\frac{1}{6}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}\)
\(=\frac{1.2.3.4.5}{2.3.4.5.6}=\frac{1}{6}\)
\(1\frac{1}{2}\times1\frac{1}{3}\times1\frac{1}{4}\times1\frac{1}{5}\)
\(=\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\frac{6}{5}\)
\(=\frac{6}{2}=3\)