1:
\(\Leftrightarrow4\cdot3^x\cdot\dfrac{1}{9}+2\cdot3^x\cdot3=4\cdot3^4+2\cdot3^7\)
\(\Leftrightarrow3^x\cdot\left(\dfrac{4}{9}+6\right)=3^4\cdot\left(4+2\cdot3^3\right)\)
\(\Leftrightarrow3^x=729\)
hay x=6
2: \(\Leftrightarrow3^x\cdot4\cdot\dfrac{1}{3}+3^x\cdot2\cdot9=4\cdot3^6+2\cdot3^9\)
\(\Leftrightarrow3^x\cdot\dfrac{58}{3}=42282\)
=>3x=2187
hay x=7
Tính:
\(\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+...+\frac{2}{x^2.3x}=\frac{1}{9}\)
Tìm x biết:
a) 3 : (1 - \(\frac{3}{2}\)x) = 4 : (2 - x)
b) \(\frac{-1}{7}\) . 23 - 2x : 1\(\frac{4}{3}\) = -2x-1
c) 2.3x + 3x-1 = 7(32 + 2.62)
d) 2x - \(\frac{5}{4}\) = (3 - \(\frac{1}{2}\))(x - \(\frac{1}{2}\))
e) \(\frac{1}{2}\) . 2x + 2x+2 = 28 . 25
cho A=(\(\dfrac{1}{2^2}-1\))(\(\dfrac{1}{3^2}-1\))(\(\dfrac{1}{2^2}-1\))...........(\(\dfrac{1}{100^2}-1\)).SO sánh A với \(\dfrac{-1}{2}\)
cm 1/2- 1/2^2+1/2^3-1/2^4+1/2^5-1/2^6 <1/3
Chứng minh\(B=1-\dfrac{1}{2^2}-\dfrac{1}{3^2}-\dfrac{1}{4^2}-...-\dfrac{1}{2004^2}>\dfrac{1}{2004}\)
Chứng minh \(S=\dfrac{1}{2^2}-\dfrac{1}{2^4}+\dfrac{1}{2^6}-...+\dfrac{1}{2^{4n-2}}-\dfrac{1}{2^{4n}}+...+\dfrac{1}{2^{2002}}-\dfrac{1}{2^{2004 }}< 0.2\)
Tính :
1) C = \(\left(\dfrac{1}{200^2}-1\right)\left(\dfrac{1}{199^2}-1\right)...\left(\dfrac{1}{101^2}-1\right)\)
2) \(D=\dfrac{1}{1-\dfrac{1}{1-2^{-1}}}+\dfrac{1}{1+\dfrac{1}{1+2^{-1}}}\)
cm 1/2- 1/2^2+1/2^3-1/2^4+1/2^5-1/2^6 <1/3
hepl
Tính
A = ( 1 - 1/1+2 ) ( 1 - 1/1+2+3 )( 1 - 1/1+2+3+4 ) ....... ( 1 - 1/1+2+3+....+99 )( 1 - 1/1+2+3+....+100 )
(1-1/1+2)(1-1/1+2+3)(1-1/1+2+3+4)+.......+(1-1/1+2+3+....+2012)
CMR: s=1/2^2 -1/2^4 +...+1/2^4n-2+...+1/2^2002-1/2^2004
