![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
2A = 2^18 - 2^17 - 2^15 - 2^14 - 2^13 - ... - 2^2 - 2
2A - A = A = ( 2^18 - 2^17 - 2^16 - 2^15 - 2^14 - 2^13 - ... - 2^2 - 2 ) - ( 2^17 - 2^16 - 2^15 - 2^14 - 2^13 - ... -2 - 1 )
A = 2^18 - 2^17 - 2^16 - 2^15 - 2^14 - 2^13 - ... - 2^2 - 2 - 2^17 + 2^16 + 2^15 + 2^14 + 2^13 + ... + 2 + 1
A = 2^18 - 2^17 - 2^17 + 1
A = 2^18 - 2 . 2^17 + 1
A =2^17- 2^16-...-2-2^0
Ax2= 2^18-2^17-.....-2^2-2^1
Ax2-A=2^18-2^17-...-2^2-2^1-2^17+2^16+....+2^1+1
A=2^18-2^17-2^17+1
A=2^18-2^17X2+1
A=2^18-2^18+1
A=0+1
A=1
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(20^2+18^2+16^2+......+4^2+2^2\right)-\left(19^2+17^2+.....+3^2+1^2\right)\)
\(=20^2-19^2+18^2-17^2+......+2^2-1^2\)
\(=\left(20-19\right)\left(20+19\right)+\left(18-17\right)\left(18+17\right)+.......+\left(2-1\right)\left(2+1\right)\)
\(=39+35+....+7+3\)
\(=\left(39+3\right)\left[\left(39-3\right):4+1\right]:2=210\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A = (202 + 182 + 162 +...+ 42 + 22) - (192 + 172 + 152 + ...+ 32 + 12)
= (202 - 192) + (182 - 172) + .......... + (42 - 32) + (22 - 12)
= (20 - 19)(20 + 19) + (18 - 17)(18 + 17) + ............ + (4 - 3)(4 + 3) + (2 - 1)(2 + 1)
= 20 + 19 + 18 + 17 + ............ + 4 + 3 + 2 + 1
= 20.21:2 = 210
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A = 217 - 216 - 215 - ... - 22 - 2 - 1
=> 2A = 218 - 217 - 216 - ... - 23 - 22 - 2
=> 2A - A = (218 - 217 - 216 - ... - 23 - 22 - 2) -(217 - 216 - 215 - ... - 22 - 2 - 1)
=> A = 218 - 1
Đặt \(A=2^{17}-2^{16}-2^{15}-...-2^2-2-1\)
\(\Rightarrow2A=2^{18}-2^{17}-2^{16}-...-2^3-2^2-2=2^{17}-2^{16}-...-2^2-2=A+1\)
\(\Rightarrow A=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A = 217 - 216 - 215 - ... - 22 - 2 - 1
=> 2A = 218 - 217 - 216 - ... - 23 - 22 - 2
=> 2A - A = (218 - 217 - 216 - ... - 23 - 22 - 2) -(217 - 216 - 215 - ... - 22 - 2 - 1)
=> A = 218 - 1
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=2^{17}-\left(1+2+2^2+...+2^{16}\right)\)
đặt \(1+2+2^2+...+2^{16}=B\Rightarrow A=2^{17}-B\)
\(B=1+2+2^2+...+2^{16}\)
\(2B=2+2^2+2^3+...+2^{17}\)
\(B=2B-B=\left(2+2^2+...+2^{17}\right)-\left(1+2+...+2^{16}\right)\)
\(B=2^{17}-1\)
\(A=2^{17}-B=2^{17}-\left(2^{17}-1\right)=2^{17}-2^{17}+1=1\)
Vậy A=1
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
Ta có:
\(A=9x^4-15x^3-6x^2+5=3x^2\left(3x^2-5x\right)-6x^2+5=3x^2.2-6x^2+5=6x^2-6x^2+5=5\)
Vậy, \(A=5\)
Bài 2: Ta có:
\(3^{15}+3^{16}+3^{17}=3^{15}+3^{15}.3+3^{15}.3^2=3^{15}.\left(1+3+3^2\right)=3^{15}.13\)
\(\Rightarrow3^{15}.13\) chia hết cho \(13\)
Do đó: \(3^{15}+3^{16}+3^{17}\) chia hết cho \(13\)