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\(\left(-4,3.1,1+1,1.4,5\right):\left(-0,5:0,05+10,01\right)\)
\(=\left[1,1\left(-4,3+4,5\right)\right]:\left(-10+10,01\right)\)
\(=\left[1,1.0,2\right]:\left(0,01\right)\)
\(=0,22:0,01\)
\(=22\)
\(6.5+1.2+3.5-5.2+6.5-4.8\)
\(=30+2+15-10+30-32\)
\(=\left(30+2\right)+\left(15-10+30\right)-32\)
\(=32+35-32\)
\(=\left(32-32\right)+35\)
\(=0+35\)
\(=35\)
ta có : \(A=6.7+6.7^2+6.7^3+...+6.7^{100}\)
\(\Rightarrow7A=7.\left(6.7+6.7^2+6.7^3+...+6.7^{100}\right)\)
\(7A=6.7^2+6.7^3+6.7^4+...+6.7^{101}\)
\(\Rightarrow7A-A=6A=\left(6.7^2+6.7^3+6.7^4+...+6.7^{101}\right)-\left(6.7+6.7^2+6.7^3+...+6.7^{100}\right)\)
\(6A=6.7^{101}-6.7=6\left(7^{101}-7\right)\Leftrightarrow A=7^{101}-7\)
vậy \(A=7^{101}-7\)
ta có : \(B=6.5-6.5^2+6.5^3-...+6.5^{99}-6.5^{100}\)
\(\Rightarrow5B=5\left(6.5-6.5^2+6.5^3-...+6.5^{99}-6.5^{100}\right)\)
\(5B=6.5^2-6.5^3+6.5^4-...+6.5^{100}-6.5^{101}\)
\(\Rightarrow5B+B=6B=6.5^2-6.5^3+6.5^4-...+6.5^{100}-6.5^{101}+6.5-6.5^2+6.5^3-...+6.5^{99}-6.5^{100}\)
\(6B=6.5-6.5^{101}=6.\left(5-5^{101}\right)\Leftrightarrow B=5-5^{101}\)
vậy \(B=5-5^{101}\)
\(A=6\cdot7+6\cdot7^2+6\cdot7^3+...+6\cdot7^{100}\\ =6\cdot\left(7+7^2+7^3+...+7^{100}\right)\\ =\left(7-1\right)\cdot\left(7+7^2+7^3+...+7^{100}\right)\\ =\left(7-1\right)\cdot7+\left(7-1\right)\cdot7^2+\left(7-1\right)\cdot7^3+...+\left(7-1\right)\cdot7^{100}\\ =7^2-7+7^3-7^2+7^4-7^3+...+7^{101}-7^{100}\\ =7^{101}-7=7\cdot\left(7^{100}-1\right)\)
\(B=6\cdot5-6\cdot5^2+6\cdot5^3-...+6\cdot5^{99}-6\cdot5^{100}\\ =6\cdot\left(5-5^2+5^3-...+5^{99}-5^{100}\right)\\ =\left(5+1\right)\cdot\left(5-5^2+5^3-...+5^{99}-5^{100}\right)\\=\left(5+1\right)\cdot5-\left(5+1\right)\cdot5^2+\left(5+1\right)\cdot5^3-...+\left(5+1\right)\cdot5^{99}-5^{100}\\ =5^2+5-5^3-5^2+5^4+5^3+...+5^{100}+5^{99}-5^{101}-5^{100}\\ =5-5^{101}\\ =5\cdot\left(1-5^{100}\right)\)
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a) 6,3 + (-3,7) + 2,4 + (-0,3)
= (6,3 + 2,4) + [-3,7 + (-0,3)]
= 8,7 + (-4)
= 4,7
b) (-4,9) + 5,5 + 4,9 + (-5,5)
= (-4,9 + 4,9) + [5,5 + (-5,5)]
= 0 + 0
= 0
c) 2,9 + 3,7 + (-4,2) + (-2,9) + 4,2
= [2,9 + (-2,9)] + (-4,2 + 4,2) + 3,7
= 0 + 0 + 3,7
= 3,7
d) (-6,5) . 2,8 + 2,8 . (-3,5)
= 2,8 . [-6,5 + (-3,5)]
= 2,8 . (-10)
= -28.
\(A=\left|3,7-x\right|+2,5\ge2,5\)
\(MinA=2,5\Leftrightarrow3,7-x=0\Rightarrow x=3,7\)
\(B=\left|x+1,5\right|+4,5\ge4,5\)
\(MinB=4,5\Leftrightarrow x+1,5=0\Rightarrow x=-1,5\)
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