Thực hiện phép tính:
( 1 - 2/ 2 . 3) . (1 - 2/ 3 . 4) . .... . ( 1- 2/ 99 . 100)
( -2) . ( -1 và 1/2) . ( -1 và 1/3) . ..... . (-1 và 1/2008)
( Trong đó / nghĩa là phần, ai bít làm giúp mk vs)
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29 tháng 6 2016
\(=\frac{2-1}{\sqrt{2}+1}+\frac{3-2}{\sqrt{3}+\sqrt{2}}+\frac{4-3}{\sqrt{4}+\sqrt{3}}+...+\frac{100-99}{\sqrt{100}+\sqrt{99}}.\)
\(=\frac{\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)}{\sqrt{2}+1}+\frac{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)}{\sqrt{3}+\sqrt{2}}+\frac{\left(\sqrt{4}+\sqrt{3}\right)\left(\sqrt{4}-\sqrt{3}\right)}{\sqrt{4}+\sqrt{3}}+...\)
\(=\sqrt{2}-1+\sqrt{3}-\sqrt{2}+\sqrt{4}-\sqrt{3}+...+\sqrt{100}-\sqrt{99}\)
\(=\sqrt{100}-1=10-1=9.\)
NT
1
TT
3 tháng 2 2021
\(\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right).....\left(1-\dfrac{1}{2008^2}\right)\)
\(=\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}....\dfrac{2008^2-1}{2008^2}\)
\(=\dfrac{1.3}{4}.\dfrac{2.4}{9}.\dfrac{3.5}{16}....\dfrac{2007.2009}{2008^2}\)
\(=\left(\dfrac{1.2.3...2007}{2.3.4....2008}\right).\dfrac{3.4.5...2009}{2.3.4...2008}\)
\(=\dfrac{1}{2008}.\dfrac{2009}{2}=\dfrac{2009}{4016}\)
5 tháng 5 2015
\(a.\frac{2}{3}+\frac{1}{5}\cdot\frac{10}{7}\)
\(=\frac{2}{3}+\frac{1\cdot2}{1\cdot7}\)
\(=\frac{2}{3}+\frac{2}{7}=\frac{2\cdot7}{21}+\frac{2\cdot3}{21}=\frac{14}{21}+\frac{6}{21}=\frac{20}{21}\)
\(b.\frac{2}{7}\cdot\frac{4}{7}+\frac{2}{7}\cdot\frac{3}{7}\)
\(=\frac{2}{7}\cdot\left(\frac{4}{7}+\frac{3}{7}\right)\)
\(=\frac{2}{7}\cdot\frac{7}{7}=\frac{2}{7}\cdot1=\frac{2}{7}\)
\(c.\left[-\frac{1}{4}+\frac{3}{10}\right]:\left(-\frac{3}{5}\right)-\frac{7}{6}\)
\(=\left[-\frac{5}{20}+\frac{6}{20}\right]:\left(-\frac{3}{5}\right)-\frac{7}{6}\)
\(=\frac{1}{20}:\left(-\frac{3}{5}\right)-\frac{7}{6}\)
\(=\frac{1}{20}\cdot\left(-\frac{5}{3}\right)-\frac{7}{6}\)
\(=\frac{1\cdot\left(-1\right)}{4\cdot3}-\frac{7}{6}\)
\(=\left(-\frac{1}{12}\right)-\frac{7}{6}=\left(-\frac{1}{12}\right)-\frac{14}{12}=-\frac{15}{12}\)
bài 2 :a) \(2x-2\frac{2}{7}=2\frac{5}{7}\)
\(2x=2\frac{5}{7}-2\frac{2}{7}\)
\(2x=\left(2-2\right)+\left(\frac{5}{7}-\frac{2}{7}\right)\)
\(2x=0+\frac{3}{7}\)
\(2x=\frac{3}{7}\)
\(x=\frac{3}{7}:2=\frac{3}{7}\cdot\frac{1}{2}=\frac{3}{14}\)
\(b.\frac{17}{13x}=\frac{4}{39}\)
\(\Rightarrow13x\cdot4=17\cdot39\)
\(\Rightarrow13x\cdot4=663\)
\(\Rightarrow13x=663:4\)
\(\Rightarrow13x=165,75\)
\(\Rightarrow x=165,75:13\)
\(\Rightarrow x=12,75\)
\(****nha!!!!!!!!!!!!\)
