Bạn tham khảo :
$A$ $= 1 +2+2^2+2^3+2^4+.......+2^{56} = ( 1 + 2 + 2^2 ) + ( 2^2 + 2^3 + 2^4) + .... + (2^{54} + 2^{55} + 2^{56} ) = ( 1+2+2^2) . 1 + 2^2( 1 + 2 + 2^2) .... + 2^{54} ( 1 + 2 + 2^2) = 7 + 7. 2^2 + ... + 7. 1^54 = 7 ( 1 + 2^2 + ... + 2^{54})$
Vì $7 \vdots 7 ⇒ 7 ( 1 + 2^2 + ... + 2^54 ) \vdots 7 ⇒A = 1 +2+2^2+2^3+2^4+.......+2^56 \vdots 7$
$B = - 2+4+(-6)+8+(-10)+...+100 = (-2 + 4 ) + ( -6 + 8 ) + (-10 + 12 ) + ... + (-98 + 100 ) = 2 + 2 + 2 + ... + 2 = 2.25 = 50 $
$C =1+3^2+3^4+3^6+...+3^{100} = ( 1+ 3^2 + 3^4 ) + (3^6 + 3^8 + 3^10 ) + ...+ (3^{96} +3^{98} + 3^{100} = 91 . 3^6 ( 1 + 2 + 3^4) + ... + 3^{96} ( 1 + 2 + 3^4) = 91 . 3^6 . 91 + ... 3^{96} . 91 = 91 ( 1 + 3^6 + ... + 3^{96} )$
Vì $91 \vdots 91 ⇒ 91 ( 1 + 3^6 + ... + 3^96 ) \vdots 91 ⇒C =1+3^2+3^4+3^6+...+3^{100} \vdots 91$
