Question

Tính \(A=1+10+10^2+10^3+.....+10^{100}\)

Answer 1

A = 1 + 10 + 10²  + ... + 10¹⁰⁰

10A - A  = ( 10 + 10²+ 10³ + ... + 10¹⁰¹) - ( 1 + 10 + 10²+ ... + 10¹⁰⁰ )

9A = 10¹⁰¹ - 1

=> A = 10¹⁰¹ - 1/9

Answer 2

\(A=1+10+10^2+10^3+......+10^{100}\)

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

\(10-A=10^{101}-1\)

\(9A=10^{101}-1=>A=\frac{10^{101}-1}{9}\)