Question

A = \(\dfrac{1+7+7^2+7^3+7^4+....+7^{2013}}{1-7^{2014}}\)

Tính A.

Answer 1

\(A=\dfrac{1+7+7^2+7^3+7^4+...+7^{2013}}{1-7^{2014}}\)

\(\Rightarrow7A=\dfrac{7+7^2+7^3+7^4+7^5+...+7^{2014}}{1-7^{2014}}\)

\(\Leftrightarrow7A-A=\dfrac{\left(7+7^2+7^3+...+7^{2014}\right)-\left(1+7+7^2+...+7^{2013}\right)}{1-7^{2014}}\) \(\Leftrightarrow6A=\dfrac{7+7^2+7^3+...+7^{2014}-1-7-7^2-....-7^{2013}}{1-7^{2014}}\) \(\Leftrightarrow6A=\dfrac{7^{2014}-1}{1-7^{2014}}\)

\(\Leftrightarrow A=\dfrac{7^{2014}-1}{1-7^{2014}}.\dfrac{1}{6}\)

\(\Rightarrow A=\dfrac{7^{2014}-1}{6-6.7^{2014}}\)

Answer 2

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