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1 tháng 12 2017

Ta có : A = (51+52+53)+(54+55+56)+...+(528+529530)

          A = 155 + 53.(51+52+53)+...+527.(51+52+53)

          A = 155 + 53. 155+...+527.155

          A = 155.(1+53+...+527)  chia hết cho 155 

Vậy A chia hết cho 155

(5+52+53)+(54+55+56)+...+(528+529+530

= 155 +53(5+52+53)+...+527(5+52+53

=155+53.155+...+527.155 

=155(1+53+..+527) chia hết cho 155

27 tháng 12 2017

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28 tháng 12 2017

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10 tháng 8 2017

2.Gọi số cần tìm là \(x\left(x\ne0,x>9\right)\)

Ta có:

\(53=mx+2\left(m\in N\right)\\ \Rightarrow51=mx\\ \Rightarrow x\inƯ\left(51\right)\left(1\right)\\ 77=nx+9\left(n\in N\right)\\ \Rightarrow68=nx\\ \Rightarrow x\inƯ\left(68\right)\left(2\right)\)

Từ (1) và (2) ta có:

\(x\inƯC\left(51,68\right)\)

\(51=3\cdot17\\ 68=2^2\cdot17\\ \Rightarrow\text{ƯCLN}\left(51,68\right)=17\\ ƯC\left(51,68\right)=Ư\left(17\right)=\left\{1;17\right\}\)

Vì x > 9 nên x = 17

Vậy số chia là 17

10 tháng 8 2017

3. Làm câu b trước, các câu kia trả lời tương tự hoặc áp dụng điều đã chứng minh

b,

\(a+a^2+a^3+a^4+...+a^{29}+a^{30}\\ =\left(a+a^2\right)+\left(a^3+a^4\right)+...+\left(a^{29}+a^{30}\right)\\ =a\left(1+a\right)+a^3\left(1+a\right)+...+a^{29}\left(1+a\right)\\ =\left(1+a\right)\left(a+a^3+...+a^{29}\right)⋮a+1\)

Vậy \(a+a^2+a^3+a^4+...+a^{29}+a^{30}⋮a+1\) với a thuộc N

9 tháng 9 2018

S = 5 + 52 + 53 + 54 + .......... + 599

a)  S = ( 5 + 52 + 53 ) + ( 54 + 55 + 56 ) + .... + ( 597 + 598 + 599 )

    = 5. ( 1 + 5 + 52 ) + 54 . ( 1 + 5 + 52 ) + .... + 597 . ( 1 + 5 + 52 )

     = ( 1 + 5 + 52 ). ( 5 + 54 + .. + 597 )

      = 31 . ( 5 + 54 + .... + 597 ) chia hết cho 31 ( đpcm )

c ) 5S = 52 + 53 + .. + 5100

=> 5S - S = 4S = 5100 + 599 + ........ + 53 + 52 - 5 - 52 - 53 - ..... - 599

                         = 5100 - 5 

25x - 5 = 4S

=> 25x - 5 = 5100 - 5

=> 25x = 5100

=> 25x = ( 52 )50

=> 25x = 2550

=> x = 50

Vậy  x = 50

Câu b quên cách làm rồi     

a) S=5+52+53+54+...+599

=(5+52+53)+(54+55+56)+...+(597+598+599)

=5(1+5+52)+54(1+5+52)+...+597(1+5+52)

=5.31+54.31+...+597.31

=31(5+54+...+597)⋮31(đpcm)

b) S=5+52+53+54+...+599

=5+(52+53)+(54+55)+...+(598+599)

=5+5(5+52)+53(5+52)+...+597(5+52)

=5+5.30+53.30+...+597.30

=5+30.(5+53+...+597)

Mà 5⋮̸30 nên S⋮̸30(đpcm)

c) Ta có: 5S=52+53+54+55+...+5100

5S−S=(52+53+54+55+...+5100)−(5+52+53+54+...+599)

4S=5100−5

⇒25x−5=5100−5

⇒25x=5100

⇒25x=2550

⇒x=50

10 tháng 4 2018

\(5+5^2+5^3+...5^{29}+5^{30}\)

\(=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{29}+5^{30}\right)\)

\(=5\left(1+5\right)+5^3\left(1+5\right)+...+5^{29}\left(1+5\right)\)

\(=5.6+5^3.6+...+5^{29}.6⋮6\)

8 tháng 6 2018

b ) B = 5 + 52 + ... + 57 . 58

= ( 5 + 52 ) + ... + ( 57 . 5)

= 5 . ( 1 + 5 ) + ... + 57 . ( 1 + 5 )

= 5 . 6 + ... + 57 . 6

= 6 . ( 5 + ... + 57 ) \(⋮\)6

8 tháng 6 2018

a ) 53! - 51!

= 51! . ( 52 . 53 - 1 )

= 51! . 2755 

mà 2755 \(⋮\)29 => 51! . 2755 

Vậy 53! - 51!  \(⋮\)29

9 tháng 4 2018
Giúp tui nọi người ơi
13 tháng 4 2018

Ta có :5+5^2+5^3+...+5^29+5^30

=(5+5^2)+(5^3+5^4)+.....+(5^29+5^30)

=(5+5^2)+5^2(5+5^2)+.....+5^28(5+5^2)

=30+5^2.30+.....+5^28.30

Vì 30 chia hết cho 6 =>30+5^2.30+.....+5^28.30 chia hết cho 6  

hay 5+5^2+5^3+...+5^29+5^30 chia hết cho 6

30 tháng 9 2015
 
 

 



a) Theo đề bài ra, ta có : ab¯¯¯+ba¯¯¯=(10a+b)+(10b+a)=11a+11b=11(a+b)� ��11

b) Theo đề bài ra ta có : ab¯¯¯−ba¯¯¯=(10a+b)−(10b+a)=10a+b−10b� ��a=9a−9b=9(a−b)⋮9

9 tháng 1 2017

A=5+5^2+5^3+...+5^2013

A=(5+5^2+5^3)+(5^4+5^5+5^6)+...+(5^2011+2^2012+5^2013)

A=155+5^4*(5+5^2+5^3)+...+5^2011*(5+5^2+5^3)

A=155+5^4*155+...+5^2011*155

A=155*(5^4+...+5^2011) chia hết cho 155

tk mk nha

thanks