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A =(1/2 +1)×(1/3 +1)×(1/4 +1)×....×(1/99 +1)
=3/2x4/3x...............x100/99
=2-1/99
=197/99
A= \(\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot.....\cdot\frac{100}{99}\)
A=\(\frac{\left(3\cdot4\cdot5\cdot....\cdot99\right)\cdot100}{2\cdot\left(3\cdot4\cdot5\cdot...\cdot99\right)}\)
A=\(\frac{100}{2}=50\)
\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{97\cdot99}\)
\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\)
=> \(\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)>\(\frac{32}{100}\)=32%
a. \(A=\dfrac{1}{2}\cdot\dfrac{2}{3}+\dfrac{5}{10}\) \(B=\dfrac{7}{8}-\dfrac{1}{4}\cdot\dfrac{3}{2}\)
\(=\dfrac{1}{3}+\dfrac{1}{2}\) \(=\dfrac{7}{8}-\dfrac{3}{8}\\ =\dfrac{1}{2}\)
\(\Rightarrow A>B\)
b. \(C=\dfrac{2}{3}\cdot\dfrac{4}{5}+\dfrac{8}{15}-\dfrac{1}{15}\)
\(=\dfrac{8}{15}+\dfrac{7}{15}\\ =\dfrac{15}{15}\\ =1\)
\(D=\dfrac{1}{2}\cdot\dfrac{5}{6}+\dfrac{2}{3}\cdot\dfrac{3}{4}\)
\(=\dfrac{5}{12}+\dfrac{6}{12}\\ =\dfrac{11}{12}\)
\(\Rightarrow C>D\)
\(C=\left(1+\frac{2}{3}\right)\cdot\left(1+\frac{2}{5}\right)\cdot\left(1+\frac{2}{7}\right)\cdot\cdot\cdot\cdot\cdot\left(1+\frac{2}{2009}\right)\cdot\left(1+\frac{2}{2011}\right)\)
\(C=\frac{5}{3}\cdot\frac{7}{5}\cdot\frac{9}{7}\cdot\cdot\cdot\cdot\cdot\frac{2011}{2009}\cdot\frac{2013}{2011}\)
\(C=\frac{5\cdot7\cdot9\cdot\cdot\cdot\cdot\cdot2011\cdot2013}{3\cdot5\cdot7\cdot\cdot\cdot\cdot\cdot2009\cdot2011}\)
\(C=\frac{2013}{3}\)
A = (4+\(\frac{1}{5}\)) . \(\frac{18}{19}\)+ (2+\(\frac{8}{5}\)) . \(\frac{21}{5}\)
A= \(\frac{21}{5}\).18/19 + 18/5 . 21/5
A= 21/5 (18/19 + 18/5)
A= 21/5 . 432/95
A= 9288/95
b= 25/2. (3+2/7) - 23/7. (5 + 1/2)
b= 25/2 . 23/7 - 23/7 . 11/2
b= 23/7 (25/2 -11/2)
b=23/7 . 7
b= 23
a: \(A=\dfrac{2}{3}-4\cdot\dfrac{5}{4}=\dfrac{2}{3}-5=-\dfrac{13}{3}\)
b: \(B=\dfrac{-2+5}{6}\cdot11-7=\dfrac{11}{2}-7=-\dfrac{3}{2}\)
c: \(=1+\dfrac{2}{3}\cdot\dfrac{1}{2}+\dfrac{27}{4}+5-1\)
\(=\dfrac{1}{3}+\dfrac{27}{4}+5=\dfrac{145}{12}\)
d: \(D=\dfrac{2}{3}\cdot\dfrac{2}{5}-\dfrac{1}{5}\cdot\dfrac{1}{6}=\dfrac{4}{15}-\dfrac{1}{30}=\dfrac{7}{30}\)
A = 1/2 x 2/3 x.....x 2009/2010 = 1x2x3x....x2009 / 2x3x4x.........x 2010
A = 1/ 2010
vậy A = 1/ 2010
\(A=\frac{1}{2}\times\frac{2}{3}\times...\times\frac{2009}{2010}\)
\(A=\frac{1\times2\times...\times2009}{2\times3\times2010}\)
\(A=\frac{1}{2010}\)
A. |-5| . (-7) + 4 . (-9)
= 5 . (-7) + 4 . (-9)
= (-35) + (-36)
= (-71)
B. 3 . (-5)2 + 2 . (-5) - 20
= 3 . 25 + 2 . (-5) - 20
= 75 + (-10) - 20
= 65 - 20
= 45
C. (15 - 10) - 15(34 - 10)
= 15 - 10 - (15 . 34 - 15 . 10)
= 15 . 1 - 10 - 15 . 34 + 15 . 10
= 15 . (1 - 34 + 10) - 10
= 15 . (-23) - 10
= (-345) - 10
= -355
D. 1 - 2 + 3 - 4 + 5 - 6 + .... + 2009 - 2010 + 2011
= (1 - 2) + (3 - 4) + .... + (2009 - 2010) + 2011
= (-1) + (-1) + .... + (-1) + 2011
2010 : 2 = 1005
= (-1) . 1005 + 2011
= (-1005) + 2011
= 1006
a,\(\frac{21}{25}.\frac{11}{9}.\frac{5}{7}=\frac{21.11.5}{25.9.7}=\frac{3.7.11.5}{5^2.3^2.7}=\frac{11}{5.3}=\frac{11}{15}\)
b,\(\frac{5}{23}.\frac{17}{26}+\frac{5}{23}.\frac{9}{26}=\frac{5}{23}.\left(\frac{17}{26}+\frac{9}{26}\right)=\frac{5}{23}.1=\frac{5}{23}\)
c, \(\left(\frac{3}{29}-\frac{1}{5}\right).\frac{29}{3}=\frac{3}{29}.\frac{29}{3}-\frac{1}{5}.\frac{29}{3}=1-\frac{29}{15}=-\frac{14}{15}\)
a , \(\frac{21}{25}\times\frac{11}{9}\times\frac{5}{7}\)
\(=\frac{21\times11\times5}{25\times9\times7}\)
\(=\frac{3\times7\times11\times5}{5\times5\times3\times3\times7}\)
\(=\frac{11}{5\times3}\)
\(=\frac{11}{15}\)
b , \(\frac{5}{23}\times\frac{17}{26}+\frac{5}{23}\times\frac{9}{26}\)
\(=\frac{5}{23}\times\left(\frac{17}{26}+\frac{9}{26}\right)\)
\(=\frac{5}{23}\times\frac{26}{26}\)
\(=\frac{5}{23}\times1\)
\(=\frac{5}{23}\)
c , \(\left(\frac{3}{29}-\frac{1}{5}\right)\times\frac{29}{3}\)
\(=\frac{3}{29}\times\frac{29}{3}-\frac{1}{5}\times\frac{29}{3}\)
\(=1-\frac{29}{15}\)
mọi người giúp em với ạ em đang cần gấp lắm .
Đặt S = (-1) x ( -1)2x ....x (-1)2011
Ta có : S = ( -1 ) x ( -1)2x ....x (-1) 2011
= (-1) x 1 x....x 1
= ( -1 )
Vậy S = (-1)
( Vì (-1)2= 1 theo quy ước của máy tính nen tớ làm như trên!! Học tốt !!)