Question

Tính : A = \(1+10^2+10^4+10^6+...+10^{2016}\)

giúp mk với

Answer 1

Từ đề bài, ta có:

\(10^2A=10^2+10^4+10^6+...+10^{2018}\)

\(\Rightarrow100A-A=99A=10^{2018}-1\)

\(\Rightarrow A=\dfrac{10^{2018}-1}{99}\)

Answer 2

A = 1 + 10² + 10⁴ + 10⁶ + ... + 10²⁰¹⁶
\(\Rightarrow\)10A = 10 + 10³ + 10⁵ + ... + 10²⁰¹⁷
\(\Rightarrow\) 10A - A = 10²⁰¹⁷ - 1
\(\Rightarrow\) 9A = 10²⁰¹⁷ - 1
\(\Rightarrow\) A = \(\dfrac{10^{2017}-1}{9}\)