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C = 2 + 22 + 23 + ... + 299 + 2100
a)
C = ( 2 + 22 + 23 + 24 + 25 ) + ( 26 + 27 + 28 + 29 + 210 ) + ... + ( 296 + 297 + 298 + 299 + 2100 )
= 2( 1 + 2 + 22 + 23 + 24 ) + 26( 1 + 2 + 22 + 23 + 24 ) + ... + 296( 1 + 2 + 22 + 23 + 24 )
= 2.31 + 26.31 + ... + 296.31
= 31( 2 + 26 + ... + 296 ) chia hết cho 31 ( đpcm )
b)
C = 2 + 22 + 23 + ... + 299 + 2100
=> 2C = 2( 2 + 22 + 23 + ... + 299 + 2100 )
= 22 + 23 + ... + 2100 + 2101
=> C = 2C - C
= 22 + 23 + ... + 2100 + 2101 - ( 2 + 22 + 23 + ... + 299 + 2100 )
= 22 + 23 + ... + 2100 + 2101 - 2 - 22 - 23 - ... - 299 - 2100
= 2101 - 2
22x-1 - 2 = C
<=> 22x-1 - 2 = 2101 - 2
<=> 22x-1 = 2101 - 2 + 2
<=> 22x-1 = 2101
<=> 2x - 1 = 101
<=> 2x = 102
<=> x = 51
C=2+22+23+...+299+2100.
= 2 . ( 2+22+23+24 ) + 26 . ( 2+22+23+24 ) + ....... + 296 . ( 2+22+23+24 )
= 2 . 31 + 26 . 31 + ....... + 296 . 31
=31 . ( 2 + 26 + ..... + 296 )
\(\Rightarrow\)C=2+22+23+...+299+2100 \(⋮\)31
a)Ta có: C=2+22+23+...+2100 C=1.(2+22+23+24+25)+25.(2+22+23+24+25)+...+295.(2+22+23+24+25) C=2.31+25.2.31+...+295.2.31 C=31(2+2.25+...+2.295) =>C chia hết cho 31
a)C=2+22+23+...+2100
=2.(1+2+4+8+16)+26.(1+2+4+8+16)+...+296.+(1+2+4+8+16)
=2.31+26.31+...+296.31
=31.(2+26+...+296) chia hết cho 31
C chia hết cho 31
6) \(2\left(x-8\right)=2^2\)
\(\Rightarrow x-8=2^2:2\)
\(\Rightarrow x-8=2\)
\(\Rightarrow x=2+8\)
\(\Rightarrow x=10\)
tíc mình nha
5) 14 chia hết cho 2x+3
=>2x+3 thuộc ước 14
mà Ư(14)={1,2,7,14}
ta có
| 2x+3 | 1 | 2 | 3 | 14 |
| x | X | X | 0 | X |
vậy x=0
\(C=2+2^2+2^3+...+2^{100}\)
\(2C=2^2+2^3+...+2^{100}+2^{101}\)
\(2C-C=\left(2^2+2^3+....+2^{101}\right)-\left(2+2^2+...+2^{100}\right)\)
\(C=2^{101}-2\)
Thay \(C=2^{101}-2\)vào \(2^{2x-1}-2\)ta được:
\(2^{2x-1}-2=2^{101}-2\)
\(\Rightarrow2^{2x-1}=2^{101}-2+2\)
\(\Rightarrow2^{2x-1}=2^{101}\)
\(\Rightarrow2x-1=101\)
\(\Rightarrow2x=102\)
\(\Rightarrow x=102\div2\)
\(\Rightarrow x=51\)
Vậy x = 51.
Nhớ k nhé!
2C = 2\(^2\)+ 2\(^3\)+ 2\(^4\)+ ... + 2\(^{101}\)
2C - C = ( 2\(^2\)+ 2\(^3\)+ 2\(^4\)+ ... + 2\(^{101}\)) - ( 2 + 2\(^2\)+ 2\(^3\)+ ... + 2\(^{100}\))
C = 2\(^2\)+ 2\(^3\)+ 2\(^4\)+ ... + 2\(^{101}\)- 2 - 2\(^2\)- 2\(^3\)- ... - 2\(^{100}\)
C = ( 2\(^2\)+ 2\(^2\)) + ( 2\(^3\)- 2\(^3\)) + ( 2\(^4\)+ 2\(^4\)) + ... + (2\(^{100}\)- 2\(^{100}\)) + ( 2\(^{101}\)- 2)
C = 2\(^{101}\)- 2
Ta có :
2\(^{2x-1}\) - 2 = 2\(^{101}\)- 2
2\(^{2x-1}\)= 2\(^{101}\)
2x - 1 = 101
2x = 101 + 1 = 102
x = 102 : 2 = 51
Vậy x = 51