Question

Tính tổng: S= (-1/7)\(^0\)+(-1/7)\(^1\)+(-1/7)\(^2\)+......+(-1/7)\(^{2007}\)

Answer 1

S=

7S = 1+(−1/7)^1+(−1/7)^2+...+(−1/7)^2007

=> 7S = 7+(−1/7)^1+(−1/7)^2+...+(−1/7)^2006

=> 6S = 6-(−1/7)^2007

=> S= 1-(−1/7^2007/6)

Answer 2

\(S=\left(-\frac{1}{7}\right)^0+\left(-\frac{1}{7}\right)^1+\left(-\frac{1}{7}\right)^2+...+\left(-\frac{1}{7}\right)^{2007}\\ \Rightarrow7S=7+\left(-1\right)+\left(-\frac{1}{7}\right)^2+...+\left(-\frac{1}{7}\right)^{2006}\\ \Rightarrow7S-S=\left[7+\left(-1\right)+\left(-\frac{1}{7}\right)^2+...+\left(-\frac{1}{7}\right)^{2006}\right]-\left[1+\left(-\frac{1}{7}\right)+\left(-\frac{1}{7}\right)^2+...+\left(-\frac{1}{7}\right)^{2007}\right]\\ =7-\left(-\frac{1}{7}\right)-\left(-\frac{1}{7}\right)^{2007}\\ =\frac{50}{7}-\left(-\frac{1}{7}\right)^{2007}\\ \Rightarrow S=\frac{\frac{50}{7}-\left(-\frac{1}{7}\right)^{2007}}{6}\)