S=1+7+7^2+7^3+...+7^100+7^101

   =(1+7)+7^2(1+7)+...+7^100(1+7)

   =8+7^2.8+...+7^100.8

   =8.(1+7^2+...+7^100) chia hết cho 8 

Vậy S chia hết cho 8

a.S=4+4^2+4^3+4^4+...+4^99+4^100 chia hết cho 5

   S=(4+4^2)+(4^3+4^4)+...+(4^99+4^100)

   S=20+4^2*20+...+4^98

   S=20*(1+4^2+...+4^98) chia hết cho 5(đpcm)

 b.S=2+2^2+2^3+2^4+...+2^2009+2^2010CHIA HẾT CHO 6

    S=(2+2^2)+(2^3+2^4)+...+(2^2009+2^2010)

    S=6+2^2.*6+...+2^2008

    S=6*(1+2^2+...+2^2008)CHIA HẾT CHO 6

a)Cm A=10mũ99 cộng 104 chia hết cho hai và ba 

b)Cm B=10 mũ 100 cộng 17 chia hết cho 9

c)Cm 10 mũ 11 cộng với 8 chia hết cho 18 với n thuộc z và n bé hơn hoặc bằng 2

mong mọi người trả lời giúp mik cảm ơn các bạn

\(A=2+2^2+2^3+...+2^{100}\)

\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{99}+2^{100}\right)\)

\(A=\left(2+2^2\right)+2^2\left(2+2^2\right)+...+2^{98}\left(2+2^2\right)\)

\(A=6+2^2.6+...+2^{98}.6\)

\(A=6\left(1+2^2+...+2^{98}\right)\)

Có : \(6⋮6\)

\(\Rightarrow A=6\left(1+2^2+...+2^{98}\right)⋮6\)

\(\Rightarrow A⋮6\)

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A= 2 + 2\(^2\) + 2\(^3\) + .... + 2\(^{100}\)

A = (2 + 2\(^2\)) + (2\(^3\) + 2\(^4\)) + .... + (2\(^{99}\) + 2\(^{100}\))

\(\)A = (2 + 2\(^2\)) + 2\(^2\)(2 + 2\(^2\)) +....+ 2\(^{98}\) (2 + 2\(^2\))

A = 6 + 2\(^2\).6 + .... + 2\(^{98}\).6

A = 6 (1 + 2\(^2\) + .... + 2\(^{98}\)) \(⋮\) 6

S = 1 + 3 + 3² + 3³ + 3⁴ + 3⁵ + 3⁶ + 3⁷ + 3⁸ + 3⁹ = (1 + 3) + (3² + 3³) + (3⁴ + 3⁵) + (3⁶ + 3⁷) + (3⁸ + 3⁹) = 1.(1 + 3) + 3².(1 + 3) + 3⁴.(1 + 3) + 3⁶​.(1 + 3) + 3⁸​.(1 + 3) = (1 + 3).(1 + 3² + 3⁴ + 3⁶ + 3⁸) = 4.(1 + 3² + 3⁴ + 3⁶ + 3⁸) => S ⋮ 4. Vậy S ⋮ 4 (đpcm)

gải giúp mình với

\(A=2+2^2+2^3+.......+2^{100},\)

\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+....+\left(2^{99}+2^{100}\right)\)

\(A=\left(2+2^2\right)+2^2\left(2+2^2\right)+.....+2^{98}\left(2+2^2\right)\)

\(A=6+2^2.6+....+2^{98}.6\)

\(A=6\left(1+2^2+.......+2^{98}\right)\)

\(A=6\left(1+2^2+........+2^{98}\right)\text{⋮6}\)