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Question

Cho S=5+5^2+5^3+5^4+......+5^2012. Chính tỏ rằng S chia hết cho 65

Nguyễn Thị Hồng Nhung · Accepted Answer

$S=5+5^2+..+5^{2012}$

=$\left(5+5^2+5^3+5^4\right)+...+\left(5^{2009}+5^{2010}+5^{2011}+5^{2012}\right)$

=$780\left(1+....+5^{2008}\right)⋮65$

Hay $S⋮65\left(đpcm\right)$Câu trả lời: $S=5+5^2+..+5^{2012}$

=$\left(5+5^2+5^3+5^4\right)+...+\left(5^{2009}+5^{2010}+5^{2011}+5^{2012}\right)$

=$780\left(1+....+5^{2008}\right)⋮65$

Hay $S⋮65\left(đpcm\right)$

Phương Trâm · Answer

$S=5+5^2+5^3+5^4+...+$$5^{2012}$

$S=\left(5+5^2+5^3+5^4\right)+\left(5^5+5^6+5^7+5^8\right)+...+\left(5^{2009}+5^{2010}+5^{2011}+5^{2012}\right)$

$S=65.12+5^4.\left(5+5^2+5^3+5^4\right)+...+5^{2008}.\left(5+5^2+5^3+5^4\right)$

$S=65.12+5^4.65.12+...+5^{2008}.65.12$

$S=65.12.\left(1+5^4+...+5^{2008}\right)$

$\Rightarrow S$ chia hết cho $65$ ( Đpcm ).Câu trả lời: $S=5+5^2+5^3+5^4+...+$$5^{2012}$

$S=\left(5+5^2+5^3+5^4\right)+\left(5^5+5^6+5^7+5^8\right)+...+\left(5^{2009}+5^{2010}+5^{2011}+5^{2012}\right)$

$S=65.12+5^4.\left(5+5^2+5^3+5^4\right)+...+5^{2008}.\left(5+5^2+5^3+5^4\right)$

$S=65.12+5^4.65.12+...+5^{2008}.65.12$

$S=65.12.\left(1+5^4+...+5^{2008}\right)$

$\Rightarrow S$ chia hết cho $65$ ( Đpcm ).

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