Question

Answer 1

a: A=9+99+...+999...9(10 chữ số 9)

\(=10-1+10^2-1+\cdots+10^{10}-1\)

\(=\left(10+10^2+\cdots+10^{10}\right)-10=10^2+10^3+\cdots+10^{10}\)

=>\(10A=10^3+10^4+\cdots+10^{11}\)

=>10A-A=\(10^3+10^4+\cdots+10^{11}-10^2-10^3-\cdots-10^{10}\)

=>9A=\(10^{11}-10^2\)

=>\(A=\frac{10^{11}-100}{9}\)

b: B=1+11+...+111...1(10 chữ số 1)

\(=\frac19\left(9+99+\cdots+999\ldots9\right)\) (10 chữ số 9)

\(=\frac19\cdot A=\frac19\cdot\frac{10^{11}-100}{9}=\frac{10^{11}-100}{81}\)