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410. 813 b) 2716 : 910 c) 415. 530
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C=-7/813+496 x (-7/813)+(-7/813) x 316
=-7/813 x (1+496+316)
=-7/813 x 813
=-7
\(C=\frac{-7}{813}+496.\frac{-7}{813}+\frac{-7}{813}.316\)
\(C=\frac{-7}{813}.1+496.\frac{-7}{813}+\frac{-7}{813}.316\)
\(C=\frac{-7}{813}.\left(1+496+316\right)\)
\(C=\frac{-7}{813}.813\)
\(C=\frac{-5691}{813}=-7\)
a) \(A=1+2+2^2+...+2^{50}\)
\(\Rightarrow2A=2+2^2+...+2^{51}\)
\(\Rightarrow A=2A-A=2+2^2+...+2^{51}-1-2-2^2-...-2^{50}=2^{51}-1\)
b) \(B=1+3+3^2+...+3^{100}\)
\(\Rightarrow3B=3+3^2+...+3^{101}\)
\(\Rightarrow2B=3B-B=3+3^2+...+3^{101}-1-3-3^2-...-3^{100}=3^{101}-1\)
\(\Rightarrow B=\dfrac{3^{101}-1}{2}\)
c) \(C=5+5^2+...+5^{30}\)
\(\Rightarrow5C=5^2+5^3+...+5^{31}\)
\(\Rightarrow4C=5C-C=5^2+5^3+...+5^{31}-5-5^2-...-5^{30}=5^{31}-5\)
\(\Rightarrow C=\dfrac{5^{31}-5}{4}\)
d) \(D=2^{100}-2^{99}+2^{98}-...+2^2-2\)
\(\Rightarrow2D=2^{101}-2^{100}+2^{99}-...+2^3-2^2\)
\(\Rightarrow3D=2D+D=2^{101}-2^{100}+2^{99}-...+2^3-2^2+2^{100}-2^{99}+...+2^2-2=2^{101}-2\)
\(\Rightarrow D=\dfrac{2^{101}-2}{3}\)
a) 415 x 7 - 415 x 5 + 415 x 8
= 415 x (7 - 5 + 8)
= 415 x 10
= 4150
b) 23 x 87 + 12 x 23 + 23
= 23 x 87 + 12 x 23 + 23 x 1
= 23 x (87 + 12 + 1)
= 23 x 100
= 2300
\(4^{10}.8^{13}=2^{20}.2^{39}=2^{59}\)
\(27^{16}:9^{10}=3^{48}:3^{20}=3^{28}\)
\(\left(2^2\right)^{10}.\left(2^3\right)^{13}=2^{20}.2^{39}=2^{20+39}=2^{59}\)
\(\left(3^3\right)^{16}.\left(3^2\right)^{10}=3^{48}.3^{20}=3^{48+20}=3^{68}\)
***** cho mink di mink giai bai con lai