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\(M=1-\dfrac{5}{14}-\dfrac{5}{84}-\dfrac{5}{204}-\dfrac{5}{374}\)
\(=\dfrac{84-30-5}{84}-\dfrac{5}{204}-\dfrac{5}{374}\)
\(=\dfrac{49}{84}-\dfrac{5}{204}-\dfrac{5}{374}\)
\(=\dfrac{7}{12}-\dfrac{5}{204}-\dfrac{5}{374}\)
\(=\dfrac{7\cdot17-5}{204}-\dfrac{5}{374}=\dfrac{19}{34}-\dfrac{5}{374}=\dfrac{204}{374}=\dfrac{6}{11}\)
\(M=1-\frac{5}{\sqrt{196}}-\frac{5}{\left(2\sqrt{21}\right)^2}-\frac{\sqrt{25}}{204}-\frac{\left(\sqrt{5}\right)^2}{374}\)
\(=1-\frac{5}{14}-\frac{5}{84}-\frac{5}{204}-\frac{5}{374}\left(\text{(}2\sqrt{21}\text{)}^2=2^2.21=84\right)\)
\(=1-\frac{5}{2.7}-\frac{5}{7.12}-\frac{5}{12.17}-\frac{5}{17.22}\)
\(=1-\frac{1}{2}+\frac{1}{7}-\frac{1}{7}+\frac{1}{12}-\frac{1}{12}+\frac{1}{17}-\frac{1}{17}+\frac{1}{22}\)
\(=1-\frac{1}{2}+\frac{1}{22}\)
\(=\frac{22-11+1}{22}=\frac{12}{22}=\frac{6}{11}\)
Vậy M = 6/11.
\(A=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)...\left(\frac{1}{196}-1\right)\)
\(A=\frac{-3}{2.2}.\frac{-8}{3.3}.\frac{-15}{4.4}...\frac{-195}{14.14}\)
\(A=-\left(\frac{3}{2.2}.\frac{8}{3.3}.\frac{15}{4.4}...\frac{195}{14.14}\right)\) (có 13 thừa số, môi thừa số là âm nên kết quả là âm)
\(A=-\left(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{13.15}{14.14}\right)\)
\(A=-\left(\frac{1.2.3...13}{2.3.4...14}.\frac{3.4.5...15}{2.3.4...14}\right)\)
\(A=-\left(\frac{1}{14}.\frac{15}{2}\right)=\frac{-15}{28}\)
Giải:
\(A=1-\dfrac{5}{\sqrt{196}}-\dfrac{5}{\left(2.\sqrt{21}\right)^2}-\dfrac{\sqrt{25}}{204}-\dfrac{\left(\sqrt{5}\right)^2}{374}\)
\(\Leftrightarrow A=1-\dfrac{5}{14}-\dfrac{5}{2^2.\left(\sqrt{21}\right)^2}-\dfrac{5}{204}-\dfrac{5}{374}\)
\(\Leftrightarrow A=1-\dfrac{5}{14}-\dfrac{5}{84}-\dfrac{5}{204}-\dfrac{5}{374}\)
\(\Leftrightarrow A=\dfrac{5}{5}-\dfrac{5}{14}-\dfrac{5}{84}-\dfrac{5}{204}-\dfrac{5}{374}\)
\(\Leftrightarrow A=5\left(\dfrac{1}{5}-\dfrac{1}{14}-\dfrac{1}{84}-\dfrac{1}{204}-\dfrac{1}{374}\right)\)
\(\Leftrightarrow A=5.\dfrac{6}{55}\)
\(\Leftrightarrow A=\dfrac{6}{11}\)
Vậy giá trị của biểu thức A là \(\dfrac{6}{11}\).
Chúc bạn học tốt!
\(=2015^{\left(196-1^2\right).\left(196-2^2\right)....\left(196-196\right)}\)
\(=2015^{\left(196-1^2\right).\left(196-2^2\right)....0}\)
\(=2015^0=1\)