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Ta thấy \(A=\left(-7\right)+\left(-7\right)^2+\left(-7\right)^3+...+\left(-7\right)^{2007}\)
\(A=\left[\left(-7\right)+\left(-7\right)^2+\left(-7\right)^3\right]+...+\left[\left(-7\right)^{2005}+\left(-7\right)^{2006}+\left(-7\right)^{2007}\right]\)
\(A=-7.\left[1+\left(-7\right)+49\right]+\left(-7\right)^4.\left[1+\left(-7\right)+49\right]+...+\left(-7\right)^{2005}.\left[1+\left(-7\right)+49\right]\)
\(A=-7.43+\left(-7\right)^4.43+...+\left(-7\right)^{2005}.43\)
\(A=43\left[\left(-7\right)+\left(-7\right)^4+...+\left(-7\right)^{2005}\right]⋮43\)
Vậy A chia hết cho 43.
Sửa đề: Tính tổng:
\(A=\left(-7\right)+\left(-7\right)^2+...+\left(-7\right)^{2007}...\)
Giải:
\(A=\left(-7\right)+\left(-7\right)^2+...+\left(-7\right)^{2007}\)
\(\Rightarrow-7A=-7\)\(\left[\left(-7\right)+\left(-7\right)^2+...+\left(-7\right)^{2007}\right]\)
\(=\left(-7\right)^2+\left(-7\right)^3+...+\left(-7\right)^{2008}\)
\(\Rightarrow A-\left(-7\right)A=\left(-7\right)-\left(-7\right)^{2008}\)
\(\Rightarrow8A=-7+7^{2008}\Rightarrow A=\dfrac{-7+7^{2008}}{8}\)
Vậy \(A=\dfrac{-7+7^{2008}}{8}\)
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Ta có:
\(A=\left(-7\right)+\left(-7\right)^2+...+\left(-7\right)^{2007}\)
\(=\left[\left(-7\right)+\left(-7\right)^2+\left(-7\right)^3\right]+...+\left[\left(-7\right)^{2005}+\left(-7\right)^{2006}+\left(-7\right)^{2007}\right]\)
\(=\left(-7\right).\left[1+\left(-7\right)+\left(-7\right)^2\right]+...+\left(-7\right)^{2005}\left[1+\left(-7\right)+\left(-7\right)^2\right]\)
\(=\left(-7\right).43+...+\left(-7\right)^{2005}.43\)
\(=43.\left[\left(-7\right)+...+\left(-7\right)^{2005}\right]⋮43\) (Đpcm)
\(A=\left(-7\right)+\left(-7\right)^2+....+\left(-7\right)^{2007}\)
\(A=-\left(7+7^2+...+7^{2007}\right)\)
\(7A=-\left(7^2+7^3+....+7^{2008}\right)\)
7A-A=6A= 72008- 7
=> A= \(\frac{7^{2008}-7}{6}\)
Mình làm vậy ko biết có đúng ko nữa
A = 1 . (-7) + (-7) . (-7) + (-7) . \(^{\left(-7\right)^2}\)\(+....+1.\left(-7\right)^{2005}+\left(-7\right).\left(-7\right)^{2005}+\left(-7\right)^2.\left(-7\right)^{2005}\)
\(A=\left(-7\right).\left(1+\left(-7\right)+\left(-7\right)^2\right)+...+\left(-7\right)^{2005}.\left(1+\left(-7\right)+\left(-7\right)^2\right)\)
\(A=\left(-7\right).43+....+\left(-7\right)^{2005}.43\)
\(A=43.\left(\left(-7\right)+.....+\left(-7\right)^{2005}\right)\)chia hết cho 43
Vậy A chia hết cho 43
a)S=1+(-1/7)^1+(-1/7)^2+...+(-1/7)^2007
=>7S=7+(-1/7)^1+(1/7)^2+...+(-1/7)^2006
=>(7-1)S=6-(1/7)^2007
=>S=1-(-1/7^2007/6)
Tham khảo