Question

cho S= 1+5+5^2+5^3+5^4+5^5+5^6+5^7

chứng tỏ rằng S chia hết cho 6

 

Answer 1

S = (1+5)+(5^2+5^3)+(5^4+5^5)+(5^6+5^7)

   = 6+5^2.(1+5)+5^4.(1+5)+5^6.(1+5)

   = 6+5^2.6+5^4.6+5^6.6

   = 6.(1+5^2+5^4+5^6) chia hết cho 6

=> ĐPCM

k mk nha

Answer 2

(1+5)+(5^2+5^3)+........+(5^6+5^7)

=6+5^2(1+5)+......+5^6(1+5)

=6+5^2 . 6 +.....+5^6 . 6

= 6 ( 5^2+.....+5^6)

Suy ra S chia hết cho 6

Answer 3

\(S=\left(1+5\right)+\left(5^2+5^3\right)+\left(5^4+5^5\right)+\left(5^6+5^7\right)\)

\(=6+5^2\times6+5^4\times6+5^6\times6\)

\(=6\left(1+5^2+5^4+5^6\right)\)chia hết cho 6

=> S chia hết cho 6 =>ĐPCM

Answer 4

S=1+5+5²+5³+5⁴+5⁵+5⁶+5⁷=(1+5)+(5²+5³)+(5⁴+5⁵)+(5⁶+5⁷)=(1+5)+5²(1+5)+5⁴(1+5)+5⁶(1+5)=6+5²*6+5⁴6+5⁶*6=6(1+5²+5⁴+5⁶) chia hết cho 6 (đpcm)

Vậy S chia hết cho 6

Answer 5

ta thay 1+ 5 =6 chia het cho 6

5²+5 mu 3 =5.(5+1)=5.6 chia het cho 6

...............

5 mu 6+5 mu 7=5 mu 5.(5+1) chia het cho 6       (dpcm)

Answer 6

S=6+(5^2+5^3)+(5^4+5^5)+(5^6+5^7)

S=6+25.(1+5)+5^4.(1+5)+5^6.(1+5)

S=6.(1+25+5^4+5^6)chia hết cho 6

Answer 7

5S\(=5+5^2+5^3+...+5^7+5^8\)

\(5S-S=4S=5^8-1\)

\(4S=390624\)

\(S=97656\) Mà 97656 \(⋮\)3

\(\Rightarrow S⋮3\)

Answer 8

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