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a)A<1+1/1.2 +1/2.3 +1/3.4+...+1/99.100
A<1+1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
A<2-1/100<2
b)B=1+1/2+(1/3+1/4)+(1/5+1/6+1/7+1/8)+(1/9+...+1/16)+(1/17+1/18+...+1/32)+(1/33+1/34+...+1/63+1/64)-1/64
B<1+1/2+1/2+1/2+1/2+1/2+1/2-1/64
B<1+3-1/64
B<4-1/64<6
\(10-\left[120:3-2\left(132-117\right):2\right]\)
\(=10-\left[120:3-2.15:2\right]\)
\(=10-\left[40-30:2\right]\)
\(=10-\left[40-15\right]\)
\(=10-25\)
\(=-15\)
\(163-136:\left\{150:3-320:\left[250-\left(120+15.6\right)\right]\right\}\)
\(163-126:\left\{150:3-320:\left[250-\left(120+90\right)\right]\right\}\)
\(163-126:\left\{150:3-320:\left[250-210\right]\right\}\)
\(163-126:\left\{150:3-320:40\right\}\)
\(163-126:\left\{50-8\right\}\)
\(163-126:42\)
\(163-3\)
\(160\)
hok tốt
a) 100 + (+430) + 2145 + (-530)
= 100 + [ (+430) + (-530) ] + 2145
= 100 + (-100) +2145
= 0 + 2145 = 2145
b) (-12) . 15 . 8 . (-4)
= [ (-12) . 8 ] . [ 15. (-4)]
= (-96) . (-60) = 5760
c) (+12) . 13 + 13 . (-22)
= 13. [ (+12) + (-22) ]
= 13. (-10) = -130
d) { [14 : (-2)] + 7 } : 2012
= { [ (-7) + 7 } : 2012
= 0 : 2012 = 0
e) -23 . 63 + 23 . 21 - 58 . 23
= 23 . -63 + 23 . 21 - 58.23
= 23. ( -63 + 21 - 58 )
= 23 . -100 = -2300
Hok tốt !
a) 100 + (+430) + 2145 + (-530)
=100+[430+(-530)]+2145
=100+(-100)+2145
=0+2145
=2145
b) (-12) . 15 . 8 . (-4)
=(-12.8).[15.(-4)]
=-90.(-60)
=5760
c) (+12) . 13 + 13 . (-22)
=13.[12+(-22)]
=13.(-10)
=-130
d) { [14 : (-2)] + 7 } : 2012
={-7+7}:2012
=0:2012
=0
e) -23 . 63 + 23 . 21 - 58 . 23
=23.(-63)+23.21-58.23
=23.(-63+21-58)
=23.(-100)
=-2300
a)đặt B=1/2.3+1/3.4+...+1/99.100
=1/1.2+1/2.3+1/3.4+...+1/99.100
=1-1/2+1/2-1/3+...+1/99-1/100
=1-1/100<1 (1)
Mà 1<2(2)
A =1/1+1/2.2+1/3.3+...+1/100.100<1-1/2+1/2-1/3+...+1/99-1/100 (3)
từ (1),(2),(3) =>A<2
b,c tự làm
2:
a: A=1+2+2^2+2^3+2^4
=>2A=2+2^2+2^3+2^4+2^5
=>A=2^5-1
=>A=B
b: C=3+3^2+...+3^100
=>3C=3^2+3^3+...+3^101
=>2C=3^101-3
=>\(C=\dfrac{3^{101}-3}{2}\)
=>C=D
Ta có:
\(\left\{\begin{matrix}5^{27}=\left(5^3\right)^9=125^9\\2^{63}=\left(2^7\right)^9=128^9\end{matrix}\right\}\Rightarrow5^{27}< 2^{63}\left(1\right)\)
\(\left\{\begin{matrix}2^{63}=\left(2^9\right)^7=512^7\\5^{28}=\left(5^4\right)^7=625^7\end{matrix}\right\}\Rightarrow2^{63}< 5^{28}\left(2\right)\)
Từ (1) và (2) \(\Rightarrow5^{27}< 2^{63}< 5^{28}\) (đpcm)
A) 150 - 100 : (15 . 6 - 40)
= 150 - 100 : (90 - 40)
= 150 - 100 : 50
= 150 - 2
= 148
B) 3.(63 - 58)² + 2⁷ : 2⁴ . 2⁰
= 3.5² + 2³
= 75 + 8
= 83
A) \(150-100:\left(15\cdot6-40\right)\)
\(=150-100:\left(90-40\right)\)
\(=150-100:50\)
\(=150-2\)
\(=148\)
B) \(3\left(63-58\right)^2+2^7:2^4\cdot2^0\)
\(=3\cdot5^2+2^7:2^4\)
\(=3\cdot25+2^3\)
\(=75+8\)
\(=83\)