Question

tính tổng: a = 1 + 2 + 2 mũ 2 + 2 mũ 3 + ... + 2 mũ 20

Answer 1

\(A=1+2+2^2+2^3+...+2^{20}\)
\(2A=2\left(1+2+2^2+2^3+...+2^{20}\right)\)
\(2A=2+2^2+2^3+2^4+...+2^{21}\)
\(2A-A=\left(2+2^2+2^3+2^4+...+2^{21}\right)-\left(1+2+2^2+2^3+...+2^{20}\right)\)
\(A=2^{21}-1\)

Answer 2

A=1+2+2²+2³+...+2²⁰

2A=2+2²+2³+2⁴+...+2²¹

2A-A=2²¹-1

A=2²¹-1