Chứng minh : (10n +53) chia hết cho 9
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Ta có A= 5n^3+15n^2+10n=5n^3+5n^2 +10n62+10n
=5n^29 (n+1)+10n (n+1) =(n+1).(5n^2+10n)
5n (n+1).(n+2)
do n (n=1) (n+2)chia hết cho 6
suy ra Achia hết cho 30(n thuộc z)
![](https://rs.olm.vn/images/avt/0.png?1311)
Giải:
a) A = 21 + 22 + 23 + 24 + .............. + 22010
Ta có :
Trong 1 tích chỉ cần có 1 số chia hết cho n thì tích đó chia hết cho n mà 21 \(⋮\)cả 3 và 7
=> A \(⋮\)cả 3 và 7
Vây A \(⋮\)cả 3 và 7
b) B = 31 + 32 + 33 + 34 + ............... + 22010
Ta có :
Trong 1 tích chỉ cần có 1 số chia hết cho n thì tích đó chia hết cho n
mà 32 \(⋮\)4
Vì dãy số trên là các số tự nhiên có khoảng cách là 1 nên 39 nằm trong dãy số đó mà 39 \(⋮\)13
=> B \(⋮\)cả 4 và 13
Vậy B \(⋮\)cả 4 và 13
c) C = 51 + 52 + 53 + 54 + ................... + 52010
Ta có :
Trong 1 tích chỉ cần có 1 số chia hết cho n thì tích đó chia hết cho n
mà 54 \(⋮\)6
Vì dãy số trên là các số tự nhiên có khoảng cách là 1 nên 62 nằm trong dãy số đó mà 62 \(⋮\)31
=> C \(⋮\)cả 6 và 31
Vậy C \(⋮\)cả 6 và 31
d) D = 71 + 72 + 73 + 74 + ...................... + 72010
Ta có :
Trong 1 tích chỉ cần có 1 số chia hết cho n thì tích đó chia hết cho n
mà 72 \(⋮\)8
Vì dãy số trên là các số tự nhiên có khoảng cách là 1 nên 114 nằm trong dãy số đó mà 114 \(⋮\)57
=> D \(⋮\)cả 8 và 57
Vậy D \(⋮\)cả 8 và 57
Học tốt!!!
![](https://rs.olm.vn/images/avt/0.png?1311)
\(Tacó:\hept{\begin{cases}2a+5⋮7\\7a+7⋮7\end{cases}}\Rightarrow\hept{\begin{cases}5a+2⋮7\\7⋮7\end{cases}}\Rightarrow\hept{\begin{cases}10a+4⋮7\\7⋮7\end{cases}}\)
\(\Rightarrow10a+4+7=10a+11⋮7\left(dpcm\right)\)
b, tự tương
\(a,2a+5⋮7\Leftrightarrow2a+5+28a+28⋮7\) ( vì \(28a+28⋮7\) )
\(\Leftrightarrow30a+33⋮7\)
\(\Leftrightarrow3.\left(10a+11\right)⋮7\)
\(\Leftrightarrow10a+11⋮7\) ( vì \(\left(3;7\right)=1\) )
Vậy \(2a+5⋮7\Leftrightarrow10a+11⋮7\)
Câu b bn xem lại đề hộ mk chút nhé!
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
theo mk thì cần thêm đk nữa là a;b;c thuộc Z
theo bài ra ta có :10^n+5^3=10000...0000(n chữ số 0) +125
Để 10^n+5^3 chia hết cho 9 thì 10000...0000(n chữ số 0) +125 chia hết cho 9
=>1+1+2+5 chia hết cho 9 =>9 chia hết cho 9 hay 10^n+5^3 chia hết cho 9 (ĐPCM)![](data:image/jpeg;base64,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