Tính giá trị các biểu thức:
\(\left(1-\frac{1}{3}\right).\left(1-\frac{1}{6}\right)\) \(.\left(1-\frac{1}{10}\right).\left(1-\frac{1}{15}\right)\) \(.....\left(1-\frac{1}{780}\right)\)
K
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Những câu hỏi liên quan
29 tháng 7 2017
\(B=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{780}\right)\)
\(\Rightarrow B=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{779}{780}\)
\(\Rightarrow B=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}.\frac{28}{30}...\frac{1558}{1560}\)
\(\Rightarrow B=\frac{1.4}{2.3}.\frac{2.5}{3.4}\frac{3.6}{4.5}...\frac{38.41}{39.40}\)
\(\Rightarrow B=\frac{\left(1.2.3...38\right)\left(4.5.6...41\right)}{\left(2.3.4...39\right)\left(3.4.5...40\right)}\)
\(\Rightarrow B=\frac{1.41}{39.3}=\frac{41}{117}\)
Vậy B=\(\frac{41}{117}\)
Ai thấy đúng thì k nha
23 tháng 6 2015
\(P=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}........\frac{189}{190}=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}........\frac{378}{380}\)
\(P=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}........\frac{18.21}{19.20}=\frac{1.2.3......18}{2.3.4....19}.\frac{4.5.6....21}{3.4.5....20}\)
\(P=\frac{1}{19}.\frac{21}{3}=\frac{21}{57}\)
\(A=\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{6}\right).\left(1-\dfrac{1}{10}\right)...\left(1-\dfrac{1}{780}\right)\\ =\dfrac{2}{3}.\dfrac{5}{6}.\dfrac{9}{10}...\dfrac{779}{780}\\ =\dfrac{4}{6}.\dfrac{10}{12}.\dfrac{18}{20}...\dfrac{1558}{1560}\\ =\dfrac{1.4}{2.3}.\dfrac{2.5}{3.4}.\dfrac{3.6}{4.5}...\dfrac{38.41}{39.40}=\dfrac{1.2.3..38}{2.3...39}.\dfrac{4.5...41}{3.4...40}\\ =\dfrac{1}{39}.\dfrac{41}{3}=\dfrac{41}{117}\)