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10 tháng 4 2018

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

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

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

\(=5.6+5^3.6+...+5^{29}.6⋮6\)

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

27 tháng 12 2017

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28 tháng 12 2017

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7 tháng 2 2020

Đặt : \(A=5+5^2+5^3+...+5^{30}\)

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

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

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

\(=6\left(5+5^3+...+5^{29}\right)⋮6\) (đpcm)

7 tháng 2 2020

                                                   Bài giải

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

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

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

\(=5\cdot6+5^3\cdot6+...+5^{29}\cdot6\)

\(=6\left(5+5^3+...+5^{29}\right)\text{ }⋮\text{ }6\)

\(\Rightarrow\text{ ĐPCM}\)

Ta có : A = 5 + 52 + 53 + ..... + 58

=> A = (5 + 52) + (53 + 54) + ..... + (57 + 58)

=> A = (5 + 52) + 52(5 + 52) + ..... + 56(5 + 52)

=> A = 30 + 52.30 + .... + 56.30

=> A = 30(1 + 52 + .... + 56

Vì (1 + 52 + .... + 56) là số nguyên 

Vậy A = 30(1 + 52 + .... + 56) chia hết cho 30 

8 tháng 6 2018

A=5+5^2+5^3+...+5^20

=(5+5^2)+(5^3+5^4)+...+(5^19+5^20)

=(5+5^2)+5^2(5+5^2)+...5^18(5+5^2)

=30+5^2.30+5^4.30+5^6.30+..+5^18.30

=30(1+5^2+5^4+5^6+..+5^18)(chia hết cho 30)

Vậy A là bội của 30

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

30 tháng 10 2015

a) A=5(1+5)+53(1+5)+...+5199(1+5)

  =(1+5)(5+53+....+5199) chia hết cho 6

b) A:31 dư 30 hay A-30 chia hết cho 31

Ta có A=5(1+5+52)+54(1+5+52)+57(1+5+52)+.....+598(1+5+52)

           31(5+54+57+...+599) chia hết cho 31. Nên A chia cho 31 không dư

 

20 tháng 11 2017

bai 1 (5+52) +....(57+58)

=5.(5+52) +54.(5+52) + 57(5+52)

=5.30 +54 .30 +5.30

=30.(5.54.57) chia hết cho 30

bài 2 

(3+33+35) +...(327+328+329)

=3.(3+33+35) +.....+328.(3+33 +35)
=3.273+...+328.273

=273.(3+ ......+328) chia hết cho 273