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\(A=2+2^2+2^3+2^4+........+2^{600}\)
\(\Rightarrow2A=2^2+2^3+2^4+2^5+..........+2^{601}\)
\(\Rightarrow2A-A=2^{601}-2\)
\(\Rightarrow A=2^{601}-2\)
\(A=2^2+2^3+2^4+...+2^{600}\)
\(\Rightarrow2A=2^3+2^4+2^5+...+2^{601}\)
\(2A-A=\left(2^3+2^4+2^5+...+2^{601}\right)-\left(2^2+2^3+...+2^{600}\right)\)
\(\Leftrightarrow2A-A=A=2^{601}-2^2\)
\(\frac{1}{3}+\frac{1}{2}.x=-\frac{5}{6}\)
\(< =>\frac{x}{2}=-\frac{5}{6}-\frac{2}{6}=-\frac{7}{6}\)
\(< =>-7.2=6x\)\(< =>-14=6x\)
\(< =>x=-\frac{14}{6}=-\frac{7}{3}\)
1/3 + 1/2.x = -5/6
1/2.x = -5/6 - 1/3
1/2.x = -7/6
x = -7/6 : 1/2
x = -7/3
\(4x^3=47-15\)
\(4x^3=32\)
\(x^3=\frac{32}{4}\)
\(x^3=8\)
\(\Rightarrow x=3\)
\(2.53.12+4.6.87-3.8.40\)
\(=2.53.4.3+4.6.87-3.2.4.40\)
\(=4.6.53+4.6.87-4.6.40\)
\(=4.6.\left(53+87-40\right)\)
\(=4.6.100=2400\)
đặt 1.2.3.4.5.6.7.8 = A
đặt biểu thức trên là M
ta có: M=9A - A - 8A = 0
=> M = 0
M= (1.2.3.4.5.6.7.8).9 - (1.2.3.4.5.6.7.8) - (1.2.3.4.5.6.7.8).8
=(1.2.3.4.5.6.7.8)(9-1-8)
= 0
Đặt A= \(1+2^2+2^4+...+\)\(2^{30}\)
\(\Rightarrow2^2.A=2^2.\left(1+2^2+2^4+...+2^{30}\right)\)
\(\Rightarrow4A=2^2+2^4+2^6+...+2^{30}+2^{32}\)
\(\Rightarrow4A-A=\left(2^2+2^4+2^6+...+2^{30}+2^{32}\right)-\left(1+2^2+2^4+...+2^{30}\right)\)
\(\Rightarrow3A=2^{32}-1\)
\(\Rightarrow A=\frac{2^{32}-1}{3}\)