Question

[Tề Mặc]

cho C=1+3+3²+3³+.....+3¹¹

CMR ( chứng minh rằng ) :

a) C chia hết cho 13

b) C chia hết cho 40

ai nhanh mk tk 

Answer 1

[minhduc]

\(C=1+3+3^2+.....+3^{11}.\)

\(\Rightarrow C=\left(1+3+3^2\right)+.....+\left(3^9+3^{10}+3^{11}\right)\)

\(\Rightarrow C=13+3^3.13+....+3^9.13\)

\(\Rightarrow C=13.\left(1+3^3+....+3^9\right)\)

Vì \(13⋮13\)

Do đó : \(C⋮13\)

\(C=1+3+3^2+.....+3^{11}\)

\(\Rightarrow C=\left(1+3+3^2+3^3\right)+....+\left(3^8+3^9+3^{10}+3^{11}\right)\)

\(\Rightarrow C=40+40.3^4+3^8.40\)

\(\Rightarrow C=40.\left(1+3^4+3^8\right)\)

Vì \(40⋮40\)

Do đó  \(C⋮40\)(đpcm)

Answer 2

[Thắng Hoàng]

a,C1+3+3²)+.....+3⁹,(1+3+3²)

C=13+.....+3⁹.13

C=13(1+.....+3⁹) chia hết cho 13

Vậy C chia hết cho 13

b,C=(1+3+3²+3³)+.....+3⁸(1+3+3²+3³)

   C=40+.....+3⁸+40

    C=40(1+.....+3⁸.40

    C=40(1+.....+3⁸ chia hết cho 40

Vậy C chia hết cho 40