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NT
3
N
4 tháng 12 2018
\(M=54-\frac{1}{2}.\left(1+2\right)-\frac{1}{3}.\left(1+2+3\right)-....-\frac{1}{12}.\left(1+2+...12\right)\)
\(M=54-\left[\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+....+\frac{1}{12}.\left(1+2+...+12\right)\right]\)
\(M=54-\left(\frac{1}{2}\cdot\frac{2.3}{2}+\frac{1}{3}\cdot\frac{3.4}{2}+....+\frac{1}{12}\cdot\frac{12.13}{2}\right)\)
\(M=54-\left(\frac{3}{2}+\frac{4}{2}+...+\frac{13}{2}\right)=54-44=10\)
Vậy M=10
28 tháng 6 2015
a) => \(\left(\frac{1}{3}-\frac{5}{6}x\right)^3=\frac{5}{6}-\frac{21}{54}=\frac{24}{54}=\frac{4}{9}\)
=> \(\frac{1}{3}-\frac{5}{6}x=\sqrt[3]{\frac{4}{9}}\) => \(\frac{5}{6}x=\frac{1}{3}-\sqrt[3]{\frac{4}{9}}\) => \(x=\frac{6}{5}.\left(\frac{1}{3}-\sqrt[3]{\frac{4}{9}}\right)\)
b) \(\frac{1}{3}\left(\frac{1}{2}x-1\right)^4=\frac{1}{12}-\frac{1}{16}=\frac{1}{48}\) => \(\left(\frac{1}{2}x-1\right)^4=\frac{3}{48}=\frac{1}{16}\)
=> \(\frac{1}{2}x-1=\frac{1}{2}\) hoặc \(\frac{1}{2}x-1=-\frac{1}{2}\)
=> \(\frac{1}{2}x=\frac{3}{2}\) hoặc \(\frac{1}{2}x=\frac{1}{2}\) => x = 3 hoặc x = 1
c) \(\left(1+5\right).\left(\frac{3}{5}\right)^{x-1}=\frac{54}{25}\) => \(\left(\frac{3}{5}\right)^{x-1}=\frac{9}{25}=\left(\frac{3}{5}\right)^2\)
=> x - 1= 2 => x = 3
d) \(\left(1+\left(\frac{2}{3}\right)^2\right).\left(\frac{2}{3}\right)^x=\frac{101}{243}\) => \(\frac{13}{9}.\left(\frac{2}{3}\right)^x=\frac{101}{243}\)
=> \(\left(\frac{2}{3}\right)^x=\frac{101}{243}:\frac{13}{9}=\frac{101}{351}\) (có lẽ đề sai)
2) \(\frac{1}{27^{11}}=\frac{1}{\left(3^3\right)^{11}}=\frac{1}{3^{33}}\); \(\frac{1}{81^8}=\frac{1}{\left(3^4\right)^8}=\frac{1}{3^{32}}\)
Vì 333 > 332 => \(\frac{1}{3^{33}}\) < \(\frac{1}{3^{32}}\) => \(\frac{1}{27^{11}}\) < \(\frac{1}{81^8}\)
b) \(\frac{1}{3^{99}}=\frac{1}{\left(3^3\right)^{33}}=\frac{1}{27^{33}}
LD
3 tháng 10 2019
M = 54 - \(\frac{1}{2}\). \(\frac{2.3}{2}\)- \(\frac{1}{3}\). \(\frac{3.4}{2}\)- \(\frac{1}{4}\). \(\frac{4.5}{2}\)- ... - \(\frac{1}{12}\).\(\frac{12.13}{2}\)
= 54- \(\frac{3}{2}\)- \(\frac{4}{2}\)- \(\frac{5}{2}\)- ...- \(\frac{13}{2}\)
= 54 -\(\frac{1}{2}\). ( 1+2+3+4+5+6+...+12 -1-2)
= 54 \(\frac{1}{2}\). \(\frac{13.14}{2}-3\)
=54-\(\frac{1}{2}\)(91-3)
=54-\(\frac{1}{2}\).88
= 10
Vậy M = 10
( lưu ý : \(\frac{13.14}{2}-3\)ở trong ngoặc do k bt ghi kiểu j nên để đạm vậy )
HB
0
14 tháng 3 2018
bn nhớ k nhé
b=1/2(1+2)+1/3(1+2+3)+....+1/12(1+2+3+..+12)
b=1/2*3*2/2+1/3+4*3/2+....+1/12*13*12/2
b=3/2+4/2+...+13/2
b=((13+3)*11)/2
b=8*11
b=88 vậy b=88
MS
1
N
30 tháng 11 2018
\(B=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+...+\frac{1}{12}\left(1+2+3+...+12\right)\)
\(B=1.\left(\frac{1.2}{2}\right)+\frac{1}{2}.\left(\frac{2.3}{2}\right)+\frac{1}{3}.\left(\frac{3.4}{2}\right)+....+\frac{1}{12}.\left(\frac{12.13}{2}\right)\)
\(B=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+....+\frac{13}{2}=\frac{2+3+4+....+13}{2}=\frac{90}{2}=45\)