So sánh:
\(\left(-2\right)\cdot\left(-2^2\right)\cdot\left(-2^3\right)...\left(-2^{2014}\right)\)và \(2^{2027091}\)
Những câu hỏi liên quan
\(\left(\frac{1}{2^2}\right)\cdot\left(\frac{1}{3^2}\right)\cdot\left(\frac{1}{4^2}\right)\cdot...\cdot\left(\frac{1}{2014^2}\right)\)
ta gọi biểu thức đó là A
A=1/2.2+1/3.3+...+1/2014.2014
=> A <1/1.2+1/2.3+...+1/2013/2014
=>A<1-1/2+1/2-1/3+1/3-1/4+....+1/2013-1/2014
=>A<1-1/2014
=>A<2013/2014
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Cho \(A=\left(\frac{1}{2^2}-1\right)\cdot\left(\frac{1}{3^2}-1\right)\cdot\left(\frac{1}{4^2}-1\right)\cdot...\cdot\left(\frac{1}{2014^2}-1\right)\)
\(A=\left(\frac{1}{2^2}-1\right)\cdot\left(\frac{1}{3^2}-1\right)\cdot\left(\frac{1}{4^2}-1\right)\cdot...\cdot\left(\frac{1}{2014^2}-1\right)\)
\(A=\frac{-3}{2^2}\cdot\frac{-8}{3^2}\cdot\frac{-15}{4^2}\cdot...\cdot\frac{-2014^2+1}{2014^2}\)
\(A=\frac{1\cdot\left(-3\right)}{2^2}\cdot\frac{2\cdot\left(-4\right)}{3^2}\cdot\frac{3\cdot\left(-5\right)}{4^2}\cdot...\cdot\frac{2013\cdot\left(-2015\right)}{2014^2}\)
\(A=\frac{1\cdot2\cdot3\cdot...\cdot2013}{2\cdot3\cdot4\cdot...\cdot2014}\cdot\frac{\left(-3\right)\cdot\left(-4\right)\cdot\left(-5\right)\cdot...\cdot\left(-2015\right)}{2\cdot3\cdot4\cdot...\cdot2014}\)
\(A=\frac{1}{2014}\cdot\frac{-2015}{2}\)
\(A=\frac{-2015}{4028}\)
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CHO A=\(\left(\frac{1}{2^2}-1\right)\cdot\left(\frac{1}{3^2}-1\right)\cdot\left(\frac{1}{4^2}-1\right)\cdot...\cdot\left(\frac{1}{100^2}-1\right)\). HÃY SO SÁNH A VỚI -1/2
Cho A = \(\left(\frac{1}{2^2}-1\right)\cdot\left(\frac{1}{3^2}-1\right)\cdot\left(\frac{1}{4^2}-1\right)...\left(\frac{1}{2017^2}-1\right)\cdot\left(\frac{1}{2018^2}-1\right)\) và B = \(-\frac{1}{2}\)
Hãy so sánh A và B
3. TÍnh :
P = \(1+\frac{1}{2}\cdot\left(1+2\right)+\frac{1}{3}\cdot\left(1+2+3\right)+...+\frac{1}{2014}\cdot\left(1+2+...+2014\right)\)
so sánh
\(\left(-2\right)\left(-2^2\right)\left(-2^3\right).....\left(-2^{2014}\right)\)vs\(2^{2027091}\)
Xem thêm câu trả lời
\(A=\left(\frac{1}{2^2}-1\right)\cdot\left(\frac{1}{3^2}-1\right)\cdot\cdot\cdot\left(\frac{1}{100^2}-1\right)\)
So sánh A với \(-\frac{1}{2}\)
\(A=\left(\frac{1}{2^2}-1\right)\left(\frac{1}{3^2}-1\right).....\left(\frac{1}{100^2}-1\right)\)
=> \(-A=\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)....\left(1-\frac{1}{100^2}\right)\)
\(=\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}.....\frac{100^2-1}{100^2}\)
\(=\frac{1.3}{2^2}.\frac{2.4}{3^2}.....\frac{99.101}{100^2}\)
\(=\frac{1.2....99}{2.3....100}.\frac{3.4....101}{2.3....100}\)
\(=\frac{1}{100}.\frac{101}{2}=\frac{101}{200}\)
=> \(A=-\frac{101}{200}< -\frac{1}{2}\)
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Tính:-3^2+left{-54:left[-2^8+7right]cdotleft(-2right)^2right}Tính hợp lí :31cdotleft(-18right)+31cdotleft(-81right)-31left(-12right)cdot47+left(-12right)cdot52+left(-12right)13cdotleft(23+22right)-3cdotleft(17+28right)-48+48cdotleft(-78right)+48cdotleft(-21right)
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Tính:
\(-3^2+\left\{-54:\left[-2^8+7\right]\cdot\left(-2\right)^2\right\}\)
Tính hợp lí :
\(31\cdot\left(-18\right)+31\cdot\left(-81\right)-31\)
\(\left(-12\right)\cdot47+\left(-12\right)\cdot52+\left(-12\right)\)
\(13\cdot\left(23+22\right)-3\cdot\left(17+28\right)\)
\(-48+48\cdot\left(-78\right)+48\cdot\left(-21\right)\)
`#3107.101107`
`-3^2 + {-54 \div [-2^8 + 7] * (-2)^2}`
`= -9 + [-54 \div (-256 + 7) * 4]`
`= -9 + [-54 \div (-249) * 4]`
`= -9 + (18/83 * 4)`
`= -9 + 72/83`
`= -675/83`
______
`31 * (-18) + 31 * (-81) - 31`
`= 31 * (-18 - 81 - 1)`
`= 31 * (-100)`
`= -3100`
___
`(-12) * 47 + (-12) * 52 + (-12)`
`= (-12) * (47 + 52 + 1)`
`= (-12) * 100`
`= -1200`
___
`13 * (23 + 22) - 3 * (17 + 28)`
`= 13 * 45 - 3 * 45`
`= 45 * (13 - 3)`
`= 45 * 10`
`= 450`
____
`-48 + 48 * (-78) + 48 * (-21)`
`= 48 * (-1 - 78 - 21)`
`= 48 * (-100)`
`= -4800`
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rút gọn biểu thức sau bằng cách nhanh nhấtA left(a^2+b^2-c^2right)^2-left(a^2-b^2+c^2right)^2-4a^2b^2B left(3x^3+3x+1right)cdotleft(3x^3-3x+1right)-left(3x^3+1right)^2C left(2-6xright)^2+left(2-5xright)^2+2cdotleft(6x-2right)cdotleft(2-5xright)D 5cdotleft(3x-1right)^2+4cdotleft(5x+1right)^2-12cdotleft(5x-2right)left(5x+2right)E left(3x-1right)^2+left(2x+4right)cdotleft(1-3xright)+left(x+2right)^2G left(x-1right)^3+4cdotleft(x+1right)cdotleft(1-xright)+3cdotleft(x-1right)cdotleft(x^2+x+1rig...
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rút gọn biểu thức sau bằng cách nhanh nhất
A = \(\left(a^2+b^2-c^2\right)^2-\left(a^2-b^2+c^2\right)^2-4a^2b^2\)
B = \(\left(3x^3+3x+1\right)\cdot\left(3x^3-3x+1\right)-\left(3x^3+1\right)^2\)
C = \(\left(2-6x\right)^2+\left(2-5x\right)^2+2\cdot\left(6x-2\right)\cdot\left(2-5x\right)\)
D = \(5\cdot\left(3x-1\right)^2+4\cdot\left(5x+1\right)^2-12\cdot\left(5x-2\right)\left(5x+2\right)\)
E = \(\left(3x-1\right)^2+\left(2x+4\right)\cdot\left(1-3x\right)+\left(x+2\right)^2\)
G = \(\left(x-1\right)^3+4\cdot\left(x+1\right)\cdot\left(1-x\right)+3\cdot\left(x-1\right)\cdot\left(x^2+x+1\right)\)
\(A=\left(a^2+b^2-c^2\right)^2-\left(a^2-b^2+c^2\right)^2-4a^2b^2\)
\(=\left(a^2+b^2-c^2+a^2-b^2+c^2\right)\left(a^2+b^2-c^2-a^2+b^2-c^2\right)-4a^2b^2\)
\(=2a^2.2b^2-4a^2b^2=0\)
\(C=\left(2-6x\right)^2+\left(2-5x\right)^2+2\left(6x-2\right)\left(2-5x\right)\)
\(=\left[\left(2-6x\right)+\left(2-5x\right)\right]^2\)
\(=\left[4-11x\right]^2\)
\(=16-88x+121x^2\)
chúc bn học tốt
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