Question

Cho M = 1 + 3 + 3² + 3⁴  + .....+  3⁹⁹ + 3¹⁰⁰ . Tìm Số dư khi chia M cho 13 , khi chia M cho 40.

Answer 1

Ta có M có (100-1):1+1=100 số hạng 

\(M=1+\left(3+3^2+3^3\right)+....+\left(3^{98}+3^{99}+3^{100}\right)\)

\(M=1+3\left(1+3+3^2\right)+...+3^{98}\left(1+3+3^2\right)\)

\(M=1+3.13+...+3^{98}.13\)

\(M=1+13\left(3+...+3^{98}\right)\)

Mà 13(3+...+3⁹⁸) chia hết cho 13 

=> M chia 13 dư 1

Answer 2

\(M=\left(3^1+3^2+3^3+3^4\right)+\left(3^5+3^6+3^7+3^8\right)+....+\left(3^{97}+3^{98}+3^{99}+3^{100}\right)\))\(+1\) \(M=40+3^5\times40+.....+3^{97}\times40+1\)

 \(\Rightarrow\)M chia 40 du 1

Answer 3

tổng trên có 101 số hạng

Answer 4

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