Question

Tính tổng M = \(1+\left(-2\right)+\left(-2\right)^2+...+\left(-2\right)^{2006}\)

Answer 1

M = gì cơ?

Answer 2

\(M=1+\left(-2\right)+\left(-2\right)^2+...+\left(-2\right)^{2006}\)

=> \(-2M=-2+\left(-2\right)^2+\left(-2\right)^3+...+\left(-2\right)^{2007}\)

=> \(-2M-M=-2+\left(-2\right)^2+...+\left(-2\right)^{2007}\)

- \(1+\left(-2\right)+\left(-2\right)^2+...+\left(-2\right)^{2006}\)

=>\(-3M=\left(-2\right)^{2007}-1\)

=> M = \(\dfrac{\left(-2\right)^{2007}-1}{-3}=\dfrac{-2^{2007}-1}{-3}=\dfrac{2^{2007}-1}{3}\)