Question

Ai làm nhanh nhất và chính xác mik sẽ tick cho. Help me, please.

Cho M=1+3+3²+...+3⁹⁹+3¹⁰⁰. Tìm số dư khi M chia 13;40

Answer 1

cho \(M=1+3+3^2+...+3^{99}+3^{100}\)

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

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

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

Mà \(13\left(3+3^{98}\right)⋮13\)

=> M chia cho 13 dư 1

Answer 2

+) \(M=1+3+3^2+...+3^{99}+3^{100}\)

\(\Leftrightarrow M=\left(1+3+3^2\right)+\left(3^3+3^4+3^5\right)+...+\left(3^{98}+3^{99}+3^{100}\right)\)

\(\Leftrightarrow M=\left(1+3+9\right)+3^3\left(1+3+9\right)+....+3^{98}\left(1+3+9\right)\)

\(\Leftrightarrow M=13+3^3\cdot14+....+3^{98}\cdot14\)

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

=> M chia 13 dư 0

Answer 3

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

=>\(M=1+\left(3+3^2+3^3+3^4\right)+...+\left(3^{97}+3^{98}+3^{99}+3^{100}\right)\)

=>\(M=1+3\left(1+3+3^2+3^3\right)+...+3^{96}\left(1+3+3^2+3^3\right)\)

=>\(M=4+40\left(3+...+3^{96}\right)\)

mà \(40\left(3+...+3^{96}\right)⋮40\)

=> M chia cho 40 dư 4

Answer 4

M=\(1+3+3^2+...+3^{100}\)

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

⇔M=4+32(1+3+32)+35(1+3+32)+......+398(1+3+32)⇔M=4+32(1+3+32)+35(1+3+32)+......+398(1+3+32)

⇔M=4+32.13+35.13+.........+398.13⇔M=4+32.13+35.13+.........+398.13

⇔M=4+13(32+35+..........+398)⇔M=4+13(32+35+..........+398)

Mà 13(32+35+......+398)⋮1313(32+35+......+398)⋮13

4:13(dư4)4:13(dư4)

⇔M:13(dư4)

Answer 5

thank mấy bạn nha

Answer 6

tớ cho bạn Chủ team tam giác quỷ