Question

A=1+2+2²+2³+...........+2¹⁰⁰

Answer 1

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

\(\Rightarrow2A=2+2^2+2^3+2^4+...+2^{101}\)

\(\Rightarrow A=2^{101}-1\)

Answer 2

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

\(\Rightarrow2A=2+2^2+2^3+...+2^{100}+2^{101}\)

\(\Rightarrow2A-A=2+2^2+2^3+...+2^{100}+2^{101}-\left(1+2^2+2^3+...+2^{100}\right)\)\(\Rightarrow A=2+2^2+2^3+...+2^{101}-1-2-2^2-2^3-...-2^{100}\)

\(=2^{101}-1\)

Vậy......