A=( 5+5^2)+(5^3+5^4)+(5^5+5^6)+(5^7+5^8)                                                                                                                                             A=(5+5^2)+5^2.(5+5^2)+5^4.(5+5^2)+5^6(5+5^2)                                                                                                        A=30+5^2.30+5^4.30+5^6.30                                                                                                                                                              A=30.(5^2+5^4+5^6)                                                                                                                                                                                     Mà 30 chia hết cho 30 suy ra 30.(5^2+5^4+5^6) là bội của 30

a) 7¹⁰+7⁹+7⁸

= 7⁸.7²+7⁸.7+7⁸.1

= 7⁸.(7²+7+1)

= 7⁸ .57 

=) 7¹⁰ + 7⁹+7⁸ chia hết cho 57

 goi y nhe bn nhom 3 so dau lai rui cu tiep theo se ra thua so chung la 26

ma 26 chia het cho 13

=>a la boi cua 13

\(a\left(a+2\right)-a\left(a-5\right)-7=a^2+2a-a^2+5a-7\)

\(=\left(a^2-a^2\right)+\left(2a+5a\right)-7\)

\(=7a-7\)

\(=7\left(a-1\right)⋮7\) (đpcm)

\(a\left(a+2\right)-a\left(a-5\right)-7=a^2+2a-a^2-5a-7\)

\(=\) \(\left(a^2-a^2\right)-\left(2a+5a\right)-7\)

\(=7a-7\)

\(=7\left(a-1\right)\)\(⋮\)\(7\)( đpcm) 

\(a\left(a+2\right)-a\left(a-5\right)-7=a^2+2a-a^2-5a-7\)

\(=\) \(\left(a^2-a^2\right)-\left(2a+5a\right)-7\)

\(=7a-7\)

\(=7\left(a-1\right)\)\(⋮\)\(7\)( đpcm) 

Ta có :              5 + 5² + 5³ + ........... + 5⁸ 

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

                      = 30 + 5² * 30 + ............. + 5⁶ * 30

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

           => 5 + 5² + 5³ + ............. + 5⁸ là bội của 30