Câu hỏi của Dương Thế Phương

Question

Chung to rang 2+2^2+2^3...+2^2019 chia het cho 31

❑T͙ɦáⓃⓗᵛᶰシ⒝ựɑᵛᶰシ2020ᵛᶰシ◎ · Accepted Answer

Ta có :A=2+2^2+2^3+2^4+...+2^{99}+2^{100}A=2+22+23+24+...+299+2100=> ​A=\left(2+2^2+2^3+2^4+2^5\right)+....\left(2^{96}+2^{97}+2^{98}+2^{99}+2^{100}\right)A=(2+22+23+24+25)+....(296+297+298+299+2100)​=> A=2\left(1+2+2^2+2^3+2^4\right)+...+2^{96}\left(1+2+2^2+2^3+2^4\right)A=2(1+2+22+23+24)+...+296(1+2+22+23+24)=> A=2.31+...+2^{96}.31A=2.31+...+296.31=> A=\left(2+...+2^{96}\right)31A=(2+...+296)31chia hết cho 31Câu trả lời: Ta có :A=2+2^2+2^3+2^4+...+2^{99}+2^{100}A=2+22+23+24+...+299+2100=> ​A=\left(2+2^2+2^3+2^4+2^5\right)+....\left(2^{96}+2^{97}+2^{98}+2^{99}+2^{100}\right)A=(2+22+23+24+25)+....(296+297+298+299+2100)​=> A=2\left(1+2+2^2+2^3+2^4\right)+...+2^{96}\left(1+2+2^2+2^3+2^4\right)A=2(1+2+22+23+24)+...+296(1+2+22+23+24)=> A=2.31+...+2^{96}.31A=2.31+...+296.31=> A=\left(2+...+2^{96}\right)31A=(2+...+296)31chia hết cho 31

❑T͙ɦáⓃⓗᵛᶰシ⒝ựɑᵛᶰシ2020ᵛᶰシ◎ · Answer

kick nha $Học$ $tốt$Câu trả lời: kick nha $Học$ $tốt$

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