Chung minh A la boi cua 31, A=5+5^2+5^3+5^4+5^5+...+5^2016
Chung minh rang
a) A=5+5^2+5^3+...+5^8 la boi cua 30
b) B=3+3^2+3^3+...+3^9 la boi cua 273
HELP ME !
chung to rang gia tri cua bieu thuc A=5+52+53+.....+58 la boi cua 30
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
Chung minh :710+79+98 chia het cho 57
A=5+52+53+54+.....+519+520 la boi cua 30
a) 710+79+78
= 78.72+78.7+78.1
= 78.(72+7+1)
= 78 .57
=) 710 + 79+78 chia hết cho 57
Cho A =50+51+52+53+...+599..
Chung to rang A la boi cua 13
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
Chung minh rang a thuoc Z thi a (a+2) - a(a-5)-7 la boi cua 7
\(a\left(a+2\right)-a\left(a-5\right)-7=a^2+2a-a^2+5a-7\)
\(=\left(a^2-a^2\right)+\left(2a+5a\right)-7\)
\(=7a-7\)
\(=7\left(a-1\right)⋮7\) (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)
bai1:Chứng tỏ rằng
a.A=5+5^2+5^3+5^4+...........+5^8 la boi cua 30
b.B=3+3^2+3^3+3^4+...........+3^29 la boi cua 273
Chung minh rang a thuoc Z thi a ( a+2) - a ( a-5) -7 la boi cua 7
goi a la tap hop boi chung cua a , b
goi b la tap hop uoc chung cua 13 a + 8b va 5 a+3b
chung minh rang a=b
chung to rang gia tri cua bieu thuc \(5+5^2+5^3...+5^8\) la boi cua 30
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