Question

9+99+999+...999...9(100chữ số 9)

Answer 1

tong co 45450 chu so 9

Answer 2

\(9+99+..+9999...9\)

\(=\left(10^1-1\right)+\left(10^2-1\right)+...+\left(10^{100}-1\right)\)

\(=\left(10^1+10^2+...+10^{100}\right)-100\)

Đặt \(A=10+10^2+...+10^{100}\)

\(\Rightarrow10A=10^2+10^3+...+10^{101}\)

\(\Rightarrow10A-A=\left(10^2+10^3+...+10^{101}\right)-\left(10+10^2+..+10^{100}\right)\)

\(\Rightarrow9A=10^{101}-10\)

\(\Rightarrow A=\frac{10^{101}-10}{9}\)

\(\Rightarrow9+99+999+...+999..9=\frac{10^{101}-10}{9}-100\)