Tính các tổng sau Sn=8+88+888+...+888..88 n chữ số 8

* Hướng dẫn giải

Chọn A

$S_n=\frac{8}{9}\left(9+99+999+\underset{nso9}{\underbrace{\mathrm{99...9}}}\right)$

$$\begin{gathered} =\frac{8}{9}\left(10-1+{10}^2-1+{10}^3-1+\mathrm{...}+{10}^n-1\right) \\ \begin{array}{l}=\frac{8}{9}\left[\left(10+{10}^2+{10}^3+\mathrm{...}+{10}^n\right)-n\right]\\ =\frac{8}{9}\left(10.\frac{1-{10}^n}{1-10}-n\right)\\ =\frac{80\left({10}^n-1\right)}{81}-\frac{8}{9}n.\\ \end{array} \end{gathered}$$