Tính :
a, 2^0 + 2^1 + 2^2 + 2^3 + 2^0 . 2^1. 2^2
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a) A = 20 + 21 + 22 + ... + 22015
A = 1 + 2 + 22 + ... + 22015
2A = 2.(1 + 2 + 22 + ... + 22015)
2A = 2 + 22 + 23 + ... + 22016
2A - A = (2 + 22 + 23 + ... + 22016 ) - (1 + 2 + 22 + ... + 22015)
A = 1 + 22016
b B = 1 + 31 + 32 + ... + 3200
3B = 3.(1 + 31 + 32 + ... + 3200)
3B = 3 + 32 + 33 + ... + 3201
3B - B = (3 + 32 + 33 + ... + 3201 ) - (1 + 31 + 32 + ... + 3200)
2B = 1 + 3201
B = \(\frac{1+3^{201}}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=2^0+2^1+2^2+2^3+.......+2^{100}\)
\(2A=2\left(2^0+2^1+2^2+2^3+..........+2^{100}\right)\)
\(2A=2^1+2^2+2^3+2^4+.......+2^{101}\)
\(2A-A=\left(2^1+2^2+2^3+2^4+........+2^{101}\right)-\left(2^0+2^1+2^2+2^3+..........+2^{100}\right)\)\(2A=2^{101}-2^0=2^{101}-1\)
Ta có : $A=2^0+2^1+2^2+2^3+...+2^{100}$
$=>2A=2^1+2^2+2^3+2^4+...+2^{101}$
$=>2A-A=(2^1+2^2+2^3+...+2^{101})-(2^0+2^1+2^2+...+2^{100})$
$=>A=2^101-2^0=2^101-1$
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)