Tính M=\(\frac{1}{6}+\frac{1}{18}+\frac{1}{36}+......+\frac{1}{3168}\)
Tính theo khử liên tiếp
LH
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Tính tổng sau bằng phương pháp khử liên tiếp :
\(a,P=\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+...+\frac{1}{2^{2019}}\)
\(\Rightarrow2^2P=\frac{1}{2^3}+\frac{1}{2^5}+...+\frac{1}{2^{2021}}\)
Rồi bn lấy \(2^2P-P=\frac{1}{2^{2021}}-\frac{1}{2}\)
Sai thì thôi nha! mk nghĩ thế!!!! chúc bn hok tot
Tính giá trị các biểu thức sau theo cách có dùng tính chất phép tính phân số:
a) \(\frac{2}{3} + \frac{{ - 2}}{5} + \frac{{ - 5}}{6} - \frac{{13}}{{10}};\)
b) \(\frac{{ - 3}}{7}.\frac{{ - 1}}{9} + \frac{7}{{ - 18}}.\frac{{ - 3}}{7} + \frac{5}{6}.\frac{{ - 3}}{7}\)
a)
\(\begin{array}{l}\frac{2}{3} + \frac{{ - 2}}{5} + \frac{{ - 5}}{6} - \frac{{13}}{{10}}\\ = \frac{2}{3} + \frac{{ - 5}}{6} + \frac{{ - 2}}{5} - \frac{{13}}{{10}}\\ = \left( {\frac{2}{3} + \frac{{ - 5}}{6}} \right) + \left( {\frac{{ - 2}}{5} - \frac{{13}}{{10}}} \right)\\ = \left( {\frac{4}{6} + \frac{{ - 5}}{6}} \right) + \left( {\frac{{ - 4}}{{10}} - \frac{{13}}{{10}}} \right)\\ = \frac{{ - 1}}{6} + \frac{{ - 17}}{{10}}\\ = \frac{{ - 5}}{{30}} + \frac{{ - 51}}{{30}}\\ = \frac{{ - 56}}{{30}}\\ = \frac{{ - 28}}{{15}}\end{array}\)
b)
\(\begin{array}{l}\frac{{ - 3}}{7}.\frac{{ - 1}}{9} + \frac{7}{{ - 18}}.\frac{{ - 3}}{7} + \frac{5}{6}.\frac{{ - 3}}{7}\\ = \frac{{ - 3}}{7}.\left( {\frac{{ - 1}}{9} + \frac{7}{{ - 18}} + \frac{5}{6}} \right)\\ = \frac{{ - 3}}{7}.\left( {\frac{{ - 2}}{{18}} + \frac{{ - 7}}{{18}} + \frac{{15}}{{18}}} \right)\\ = \frac{{ - 3}}{7}.\frac{{ 6}}{{18}}\\ = \frac{-1}{7}\end{array}\).
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\(\frac{12}{18}+\frac{1}{3}+\frac{1}{7}+\frac{2}{8}+\frac{27}{36}+\frac{42}{49}\) tính nhanh
\(\frac{12}{18}+\frac{1}{3}+\frac{1}{7}+\frac{2}{8}+\frac{27}{36}+\frac{42}{49}\)
\(=\frac{2}{3}+\frac{1}{3}+\frac{1}{7}+\frac{1}{4}+\frac{3}{4}+\frac{6}{7}\)
\(=\left(\frac{2}{3}+\frac{1}{3}\right)+\left(\frac{1}{7}+\frac{6}{7}\right)+\left(\frac{1}{4}+\frac{3}{4}\right)\)
\(=1+1+1\)
\(=3\)
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1/tính nhanh
a/\(A=\frac{7}{8}:\left(\frac{2}{9}-\frac{1}{18}\right)+\frac{7}{8}:\left(\frac{1}{36}-\frac{5}{12}\right)\)
b/\(B=\frac{1+0,6-\frac{3}{7}}{\frac{8}{3}+\frac{8}{5}-\frac{8}{7}}-\frac{\frac{1}{3}+0,25-\frac{1}{5}+0,125}{\frac{7}{6}+\frac{7}{8}-0,7+\frac{7}{16}}\)
A= 7/8:(4/18-1/18)+7/8:(1/36-15/36)
=7/8:1/6+7/8:(-7/18)
=7/8:(1/6+-7/18)=7/8:(3/18+-7/18)=7/8:(-2/9)=-63/18=-7/2
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Tính: \(\frac{1}{18}+\frac{1}{36}+.....+\frac{1}{29700}\)
1/18 + 1/36 + ... + 1/29700
= 1/3.6 + 1/3.12 + ... 1/3.9900
= 1/3 . 1/6 + 1/3 . 1/12 + ... + 1/3 . 1/9900
= 1/3 .(1/2.3 +1/3.4 + ... + 1/99.100)
= 1/3 .(1/2 - 1/3 +1/3 -1/4 + ... + 1/99 - 1/100)
= 1/3 .(1/2 - 1/100)
= 1/3 . 49/100
= ... (cái này bạn tự tính nhé!)
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1/18 + 1/36 + ... + 1/29700
= 1/3.6 + 1/3.12 + ... 1/3.9900
= 1/3 . 1/6 + 1/3 . 1/12 + ... + 1/3 . 1/9900
= 1/3 .(1/2.3 +1/3.4 + ... + 1/99.100)
= 1/3 .(1/2 - 1/3 +1/3 -1/4 + ... + 1/99 - 1/100)
= 1/3 .(1/2 - 1/100)
= 1/3 . 49/100
= 49/300
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Tính nhanh :
\(C=\frac{1}{3}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{57}+\frac{-1}{36}+\frac{1}{15}+\frac{-2}{9}\)
\(D=\frac{1}{2}+\frac{-1}{5}+\frac{-5}{7}+\frac{1}{6}+\frac{-3}{35}+\frac{1}{3}+\frac{1}{41}\)
\(E=\frac{-1}{2}+\frac{3}{5}+\frac{-1}{9}+\frac{1}{127}+\frac{-7}{18}+\frac{4}{35}+\frac{2}{7}\)
C = 1/3 + -3/4 + 3/5 + 1/57 + -1/36 + 1/15 + -2/9
C = ( 1/3 + 1/57 ) + ( -3/4 + -1/36 ) + ( 3/5 + 1/15 ) + -2/9
C = ( 19/57 + 1/57 ) + ( -27/36 + -1/36 ) + ( 9/15 + 1/15 ) + -2/9
C = 20/57 + -28/36 + 10/15 + -2/9
C = 20/57 + -7/9 + 2/3 + -2/9
C = ( 20/57 + 2/3 ) + ( -7/9 + -2/9 )
C = 58/57 + -1
C = 1/57
D = 1/2 + -1/5 + -5/7 + 1/6 + -3/35 + 1/3 + 1/41
D = ( 1/2 + 1/3 + 1/6 ) + ( -1/5 + -5/7 +-3/35 ) + 1/41
D = ( 3/6 + 2/6 + 1/6 ) + ( -7/35 + -25/35 + -3/35 ) + 1/41
D = 1 + -1 + 1/41
D = 1/41
E = -1/2 + 3/5 + -1/9 + 1/127 + -7/18 + 4/35 + 2/7
E = ( -1/2 + -1/9 + -7/18 ) + ( 3/5 + 4/35 ) + 1/127 + 2/7
E = ( -9/18 + -2/18 + -7/18 ) + ( 21/35 + 4/35 ) + 1/127 + 2/7
E = -1 + 5/7 + 1/257 + 2/7
E = -1 + ( 5/7 + 2/7 ) + 1/127
E = -1 + 1 + 1/127
E = 1/127
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\(C=\frac{1}{3}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{57}+\frac{-1}{36}+\frac{1}{15}+\frac{-2}{9}.\)
\(C=\left(\frac{1}{3}+\frac{3}{5}+\frac{1}{15}\right)-\left(\frac{3}{4}+\frac{1}{36}+\frac{2}{9}\right)+\frac{1}{57}\)
\(C=1-1+\frac{1}{57}\)
\(C=\frac{1}{57}\)
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D=1/2+-1/5+-5/7+1/6+-3/35+1/3+1/41
D=(1/2+1/6+1/3)-(1/5+3/35+5/7)+1/41
D=1-1+1/41
D=1/41
E=-1/2+3/5+-1/9+1/127+-7/18+4/35+2/7
E=(3/5+4/35+2/7)-(1/2+1/9+7/18)+1/127
E=1-1+1/127
E=1/127
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Tính nhanh
1, \(10\frac{5}{4}-4\frac{9}{14}-6\frac{5}{7}+\frac{7}{3}\)
2, \(\frac{29}{32}\left(\frac{41}{36}-\frac{32}{58}\right)-\frac{41}{36}\left(\frac{29}{32}+\frac{18}{41}\right)\)
tính : \(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{36}+\frac{1}{45}\)
Đặt A = 1/2 + 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/36 + 1/45
=> 1/2A = 1/4 + 1/6 + 1/12 + 1/20 + 1/30 + ... + 1/72 + 1/90
= 1/4 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + ... + 1/8.9 + 1/9.10
= 1/4 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/9 - 1/10
= 1/4 + 1/2 - 1/10
= 5/20 + 10/20 - 2/20
= 13/20
=> A = 13/20 : 1/2 = 13/10
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Đặt A = 1/2 + 1/3 + 1/6 + 1/10 + 1/15 + ... + 1/36 + 1/45
=> 1/2A = 1/4 + 1/6 + 1/12 + 1/20 + 1/30 + ... + 1/72 + 1/90
= 1/4 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + ... + 1/8.9 + 1/9.10
= 1/4 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/9 - 1/10
= 1/4 + 1/2 - 1/10
= 5/20 + 10/20 - 2/20 = 13/20
=> A = 13/20 : 1/2 = 13/10
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đặt \(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+...+\frac{1}{36}+\frac{1}{45}\)
\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{72}+\frac{1}{90}\)
\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}+\frac{1}{9.10}\)
\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(\frac{1}{2}A=\frac{1}{4}+\frac{1}{2}-\frac{1}{10}=\frac{13}{20}\)
\(\frac{1}{2}A\times2=A=2\times\frac{13}{20}=\frac{13}{10}\)
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Tính:
\(M=\left(1-\frac{1}{3}\right)\left(1\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)\left(1-\frac{1}{21}\right)\left(1-\frac{1}{28}\right)\left(1-\frac{1}{36}\right)\)