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Đặt A = 2 + 2^ 2 + 2^3 + 2^4 + ... + 2^1975
2A = 2^2 + 2^3 + 2^4 + 2^5 + ... + 2^1976)
2A - A = (2^2 + 2^3 + 2^4 + 2^5 + ... + 2^1976) - (2 + 2^ 2 + 2^3 + 2^4 + ... + 2^1975)
A = 1^ 1976 - 2
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
đặt A=22+22+23+.....+21975
=22.2+23+24+...+21975
=23+23+24+......+21975
=23.2+24+25+.........+21975
=24+24+25+26+.......+21975
.......
.......
........
=21974+21974+21975
=21974.2+21975
=21975+21975
=21975.2
=21976
vậy.....
Đặt A = 22 + 22 + 23 + 24 + ..... + 21975
2A = 23 + 23 + 24 + ..... + 21975 + 21976
2A - A = (23 + 23 + 24 + ..... + 21975 + 21976) - (22 + 22 + 23 + 24 + ..... + 21975)
A = 21976 + 23 - 22 - 22
A = 21976
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A = 22 + 22 + 23 + ... + 21975
=> 2A = 23 + 23 + 24 + ... + 21976
=> 2A - A = ( 23 + 23 + 24 + ... + 21976 ) - ( 22 + 22 + 23 + ... + 21975 )
=> A = 23 + 21976 - 22 - 22
Đặt A = 22 + 22 + 23 + ... + 21975
=> 2A = 23 + 23 + 24 + ... + 21976
=> 2A - A = ( 23 + 23 + 24 + ... + 21976 ) - ( 22 + 22 + 23 + ... + 21975 )
=> A = 23 + 21976 - 22 - 22
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1.
a) \(3^4\times3^5\times3^6=3^{4+5+6}=3^{15}\)
b) \(5^2\times5^4\times5^5\times25=5^2\times5^4\times5^5\times5^2=5^{2+4+5+2}=5^{13}\)
c) \(10^8\div10^3=10^{8-3}=10^5\)
d) \(a^7\div a^2=a^{7-2}=a^5\)
2.
\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)
\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)
\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=2^2+2^3+2^4+...+2^{20}\)
\(2A=2^3+2^4+2^5+...+2^{21}\)
\(A=2A-A=2^{21}-2^2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=2+2^2+...+2^{20}\)
\(2A=2^2+2^3+...+2^{21}\)
\(A=2^{21}-2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A = 22 + 22 + 23 + .... + 22017
2A = 23 + 23 + .... + 22017 + 22018
2A - A = (23 + 23 + .... + 22017 + 22018) - (22 + 22 + 23 + .... + 22017)
A = 23 + 22108 - 22 - 22
A = 22018
Gọi biểu thức trên là S
Ta có : S = 1 + 2 + 2^2 + 2^3 +......... 2^63
=> 2S = 2 x (1 + 2 + 2^2 + 2^3 + ........... + 2^63
=> 2S = 2 + 2^2 + 2^3 +............+ 2^63 + 2^64
------S = 1 + 2 + 2^2 + 2^3 +........+ 2^63
S = 2^64 - 1