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11 tháng 4 2017

\(B=\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{6}\right)\left(1-\dfrac{1}{10}\right)...\left(1-\dfrac{1}{780}\right)\)

\(B=\dfrac{2}{3}.\dfrac{5}{6}.\dfrac{9}{10}...\dfrac{779}{780}=\dfrac{4}{6}.\dfrac{10}{12}.\dfrac{18}{20}...\dfrac{1558}{1560}\)

\(B=\dfrac{1.4}{2.3}.\dfrac{2.5}{3.4}.\dfrac{3.6}{4.5}.....\dfrac{38.41}{39.40}\)

\(B=\dfrac{\left(1.2.3.....38\right)\left(4.5.6.....41\right)}{\left(2.3.4.....39\right)\left(3.4.5.....40\right)}=\dfrac{1.41}{39.3}=\dfrac{41}{117}\)

11 tháng 4 2017

ai giúp vs

13 tháng 3 2023

\(\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{6}\right).\left(1-\dfrac{1}{10}\right).\left(1-\dfrac{1}{15}\right)...\left(1-\dfrac{1}{780}\right)\)

\(=\dfrac{2}{3}.\dfrac{5}{6}.\dfrac{9}{10}...\dfrac{779}{780}\)

\(=\dfrac{4}{6}.\dfrac{10}{12}.\dfrac{18}{20}...\dfrac{1558}{1560}\)

\(=\dfrac{4.10.18...1558}{6.12.20...1560}\)

\(=\dfrac{41}{39}.3\)

\(=\dfrac{41}{11}\)

11 tháng 4 2017

\(A=\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{6}\right)\left(1-\dfrac{1}{10}\right)......\left(1-\dfrac{1}{780}\right)\)

= \(\dfrac{2}{3}.\dfrac{5}{6}.\dfrac{9}{10}.......\dfrac{779}{780}\)

= \(\dfrac{4}{6}.\dfrac{10}{12}.\dfrac{18}{20}.....\dfrac{1558}{1560}\)

= \(\dfrac{1.4}{2.3}.\dfrac{2.5}{3.4}.\dfrac{3.6}{4.5}......\dfrac{38.41}{39.40}\)

= \(\dfrac{1.4.2.5.3.6.....38.41}{2.3.3.4.4.5...39.40}\)

= \(\dfrac{\left(1.2.3....38\right)\left(4.5.6....41\right)}{\left(2.3.4....39\right)\left(3.4.5...40\right)}\)

= \(\dfrac{1}{39}.\dfrac{41}{3}\) = \(\dfrac{41}{117}\)

11 tháng 4 2017

làm đúng rồi đó, Thái cũng làm như mi

14 tháng 7 2017

Ta có:

\(\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{10}\right)...\left(1-\dfrac{1}{780}\right).x=1\)

\(\Leftrightarrow\dfrac{2}{3}.\dfrac{5}{6}.\dfrac{9}{10}.....\dfrac{779}{780}.x=1\)

\(\Leftrightarrow\dfrac{4}{6}.\dfrac{10}{12}.\dfrac{18}{20}.....\dfrac{1558}{1560}.x=1\)

\(\Leftrightarrow\dfrac{1.4}{2.3}.\dfrac{2.5}{3.4}.\dfrac{3.6}{4.5}.......\dfrac{38.41}{39.40}.x=1\)

\(\Leftrightarrow\dfrac{1.4.2.5.3.6.....38.41}{2.3.3.4.4.5.....39.40}.x=1\)

\(\Leftrightarrow\dfrac{\left(1.2.3.4....38\right)\left(4.5.6.7....41\right)}{\left(2.3.4.....39\right)\left(3.4.5....40\right)}.x=1\)

\(\Leftrightarrow\dfrac{1}{39}.\dfrac{41}{3}.x=1\)

\(\Leftrightarrow\dfrac{41}{117}.x=1\)

\(\Leftrightarrow x=\dfrac{117}{41}\)

Vậy ...

14 tháng 7 2017

Thanhs bạn nha

12 tháng 7 2023

a) \(A=\left(-0,75-\dfrac{1}{4}\right):\left(-5\right)+\dfrac{1}{48}-\left(-\dfrac{1}{6}\right):\left(-3\right)\)

\(A=\left(-0,75-0,25\right):\left(-5\right)+\dfrac{1}{48}-\left(-\dfrac{1}{6}\right)\cdot\dfrac{-1}{3}\)

\(A=\left(-1\right):\left(-5\right)+\dfrac{1}{48}-\dfrac{1}{18}\)

\(A=\dfrac{1}{5}+\dfrac{1}{48}-\dfrac{1}{18}\)

\(A=\dfrac{119}{720}\)

b) \(B=\left(\dfrac{6}{25}-1,24\right):\dfrac{3}{7}:\left[\left(3\dfrac{1}{2}-3\dfrac{2}{3}\right):\dfrac{1}{14}\right]\)

\(B=\left(0,24-1,24\right):\dfrac{3}{7}:\left[\left(\dfrac{7}{2}-\dfrac{11}{3}\right):\dfrac{1}{14}\right]\)

\(B=-1:\dfrac{3}{7}:\left(-\dfrac{1}{6}:\dfrac{1}{14}\right)\)

\(B=-\dfrac{7}{3}:-\dfrac{7}{3}\)

\(B=1\)

12 tháng 7 2023

a, A = (-0,75 - \(\dfrac{1}{4}\)) : (-5) + \(\dfrac{1}{48}\) - (- \(\dfrac{1}{6}\)) : (-3)

   A  = -(0,75 + 0,25): (-5) + \(\dfrac{1}{48}\) - \(\dfrac{1}{18}\)

   A = -1 : (-5) + \(\dfrac{1}{48}\) - \(\dfrac{1}{18}\)

   A = \(\dfrac{1}{5}\) + \(\dfrac{1}{48}\) - \(\dfrac{1}{18}\)

  A = \(\dfrac{53}{240}\) - \(\dfrac{1}{18}\)

 A = \(\dfrac{119}{720}\)

b, B = (\(\dfrac{6}{25}\) - 1,24): \(\dfrac{3}{7}\): [(3\(\dfrac{1}{2}\) - 3\(\dfrac{2}{3}\)): \(\dfrac{1}{14}\)]

    B = (0,24 - 1,24): \(\dfrac{3}{7}\):[(\(\dfrac{7}{2}\)-\(\dfrac{11}{3}\)): \(\dfrac{1}{14}\)]

    B = -1: \(\dfrac{3}{7}\):[ (-\(\dfrac{1}{6}\) : \(\dfrac{1}{14}\))]

   B  = -1: \(\dfrac{3}{7}\): (- \(\dfrac{7}{3}\))

B = 1 \(\times\) \(\dfrac{7}{3}\) \(\times\) \(\dfrac{3}{7}\)

B = 1

Bài 2: 

a: \(=44\cdot82-400+18\cdot44\)

\(=44\cdot100-400=4400-400=4000\)

b: \(=6^2:\left\{780:\left[390-125\cdot49+65\right]\right\}\)

\(=36:\left\{780:\left[-5670\right]\right\}\)

\(=36:\dfrac{-26}{189}=\dfrac{-3402}{13}\)

2 tháng 4 2017

2.

\(\dfrac{a}{3}-\dfrac{2}{b}=\dfrac{1}{3}\)

\(\dfrac{a\times b-3\times2}{3\times b}\)\(=\dfrac{1}{3}\)

\(\dfrac{a\times b-6}{3\times b}=\dfrac{1}{3}\)

\(\Rightarrow3\times\left(a\times b-6\right)=1\times\left(3\times b\right)\)

\(3ab-18=3b\)

\(3ab-18-3b=0\)

\(3ab-3b=18\)

\(3b\left(a-1\right)=18\)

\(18=1.18=2.9=3.6\)

\(\Rightarrow3b\left(a-1\right)=1.18=2.9=3.6\)

còn lại bạn tự làm các trường hợp ra nhé,mk lười lắmoaoa