\(2^1.2^2.2^3.....2^x=1024\Rightarrow2^{1+2+3+...+x}=2^{10}\)
\(\Rightarrow1+2+3+...+x=1024\Rightarrow x=4\)
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tìm số tự nhiên thỏa mãn điều kiện
2cdot2^2+3cdot2^3+4cdot2^4+........+ncdot2^n2^{n+11}
rút gọn : Aleft(dfrac{2}{5}-dfrac{5}{2}+dfrac{1}{10}right):left(dfrac{5}{2}-dfrac{2}{3}+dfrac{1}{12}right)
tính:Bdfrac{dfrac{1}{2}+dfrac{1}{3}+dfrac{1}{4}+......+dfrac{1}{2017}}{dfrac{2016}{1}+dfrac{2003}{2}+dfrac{2002}{3}+.......+dfrac{1}{2016}}
CMR :5a+2b⋮13Leftrightarrow9a+b⋮13left(a,bin Zright)
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tìm số tự nhiên thỏa mãn điều kiện
\(2\cdot2^2+3\cdot2^3+4\cdot2^4+........+n\cdot2^n=2^{n+11}\)
rút gọn : \(A=\left(\dfrac{2}{5}-\dfrac{5}{2}+\dfrac{1}{10}\right):\left(\dfrac{5}{2}-\dfrac{2}{3}+\dfrac{1}{12}\right)\)
tính:\(B=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+......+\dfrac{1}{2017}}{\dfrac{2016}{1}+\dfrac{2003}{2}+\dfrac{2002}{3}+.......+\dfrac{1}{2016}}\)
CMR :\(5a+2b⋮13\Leftrightarrow9a+b⋮13\left(a,b\in Z\right)\)
Rút gọn A=\(\dfrac{7^{48}\cdot5^{30}\cdot2^8-5^{30}\cdot7^{49}\cdot2^{10}}{5^{29}\cdot2^8\cdot7^{48}}\)
Tìm x biết: \(\left(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{8\cdot9\cdot10}\right)\cdot x=\frac{22}{45}\).
Có công thức cho mình thì càng tốt!
Tìm x, biết \(\left|x+\dfrac{1}{1\cdot2}\right|+\left|x+\dfrac{1}{2\cdot3}\right|+\left|x+\dfrac{1}{3\cdot4}\right|+...+\left|x+\dfrac{1}{99\cdot100}\right|=100x\)
Tính \(\text{A}\times\text{B}\), biết :
\(\text{A}=\frac{\frac{3}{10}+\frac{1}{2}-\frac{1}{6}}{\frac{1}{9}-\frac{1}{5}-\frac{1}{3}}\)
\(\text{B}=\frac{\left(3\cdot4\cdot2^{16}\right)^{^2}}{11\cdot2^{13}\cdot4^{11}-16^9}\)
Tìm n∈Z biết :
a,27n/3n
b,frac{25}{5^n}5
c,frac{81}{left(-3right)^n}-243
d,frac{1}{2}cdot2^n+4cdot2^n9cdot2^5
e,(frac{1}{3})nfrac{1}{81}
f,left(frac{-3}{4}right)^nfrac{81}{256}
g,frac{-512}{343}left(frac{-8}{7}right)^n
h,5-1*25n125
k,3-1*3n+6*3n-17*36
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Tìm n∈Z biết :
a,27n/3n
b,\(\frac{25}{5^n}\)=5
c,\(\frac{81}{\left(-3\right)^n}=-243\)
d,\(\frac{1}{2}\cdot2^n+4\cdot2^n=9\cdot2^5\)
e,(\(\frac{1}{3}\))n=\(\frac{1}{81}\)
f,\(\left(\frac{-3}{4}\right)^n=\frac{81}{256}\)
g,\(\frac{-512}{343}=\left(\frac{-8}{7}\right)^n\)
h,5-1*25n=125
k,3-1*3n+6*3n-1=7*36
1. Tính
\(\frac{2^4\cdot2^6}{\left(2^5\right)^2}-\frac{2^5\cdot15^3}{6^3\cdot10^2}\)
Chứng minh rằng:
\(\dfrac{3}{1^2\cdot2^2}+\dfrac{5}{2^2\cdot3^2}+...........+\dfrac{19}{9^2\cdot10^2}< 1\)
Tính: B= \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)