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a, A = 1 + 3 + 32 + 33 + ... + 32000
3.A = 3 + 32 + 33+ 33+... + 32001
3A - A = 3 + 32 + 33 + ... + 32001 - (1 + 3 + 32 + 33 + ... + 32000)
2A = 3 + 32 + 33 + ... + 32001 - 1 - 3 - 32 - 33 - ... - 32000
2A = 32001 - 1
A = \(\dfrac{3^{2001}-1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1) (-37) + 14 + 26 + 37
= [(-37) + 37] + 14 + 26
= 0 + 40
= 40
2) (-24) + 6 + 10 + 24
= [(-24) + 24] + 6 + 10
= 0 + 16
= 16
3) 15 + 23 + (-25) + (-23)
= 15 + (-25) + [(-23) + 23]
= -10 + 0
= -10
4) 60 + 33 + (-50) + (-33)
= 60 + (-50) + [(-33) + 33]
= 10 + 0
= 10
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left(3+3^2+3^3\right)+...+\left(3^{58}+3^{59}+3^{60}\right)\\ A=3\left(1+3+3^2\right)+...+3^{58}\left(1+3+3^2\right)\\ A=\left(1+3+3^2\right)\left(3+...+3^{58}\right)\\ A=13\left(3+...+3^{58}\right)⋮13\)
\(M=\left(2+2^2+2^3+2^4\right)+...+\left(2^{17}+2^{18}+2^{19}+2^{20}\right)\\ M=\left(2+2^2+2^3+2^4\right)+...+2^{16}\left(2+2^2+2^3+2^4\right)\\ M=\left(2+2^2+2^3+2^4\right)\left(1+...+2^{16}\right)\\ M=30\left(1+...+2^{16}\right)⋮5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=2+2^2+...+2^{20}\)
\(2A=2^2+2^3+...+2^{21}\)
\(2A-A=2^2+2^3+...+2^{21}-2-2^2-...-2^{20}\)
\(A=2^{21}-2\)
___________
\(B=5+5^2+...+5^{50}\)
\(5B=5^2+5^3+...+5^{51}\)
\(5B-B=5^2+5^3+...+5^{51}-5-5^2-...-5^{50}\)
\(4B=5^{51}-5\)
\(B=\dfrac{5^{51}-5}{4}\)
___________
\(C=1+3+3^2+...+3^{100}\)
\(3C=3+3^2+...+3^{101}\)
\(3C-C=3+3^2+...+3^{101}-1-3-3^2-...-3^{100}\)
\(2C=3^{101}-1\)
\(C=\dfrac{3^{101}-1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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) \(D=2^{100}-2^{99}+2^{98}-...+2^2-2\)
\(\Rightarrow2D=2^{101}-2^{100}+2^{99}-...+2^3-2^2\)
\(\Rightarrow3D=2D+D=2^{101}-2^{100}+2^{99}-...+2^3-2^2+2^{100}-2^{99}+...+2^2-2=2^{101}-2\)
\(\Rightarrow D=\dfrac{2^{101}-2}{3}\)
phải là thế này nè:
a, 1 + 2 + 2^2 + 2^3 + ... + 2^250
Đặt A = 1 + 2 + 2^2 + 2^3 + ... + 2^250
=> 2A = 2.(1 + 2 + 2^2 + 2^3 + ... + 2^250)
=> 2A = 2 + 2^2 + 2^3 + 2^4 + ... + 2^251
=> 2A - A = 2 + 2^2 + 2^3 + 2^4 + ... + 2^251 - (1 + 2 + 2^2 + 2^3 + ... + 2^250)
=> A = 2 + 2^2 + 2^3 + 2^4 + ... + 2^251 - 1 - 2 - 2^2 - 2^3 - ... - 2^250
=> A = 2^251 - 1
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