Question

so sánh:

2⁰+ 2¹ + 2² + 2⁴ + ...2²⁰¹⁶  và 2²⁰¹⁷

 

GIÚP EM ĐI MẤY ANH CHỊ !!!

 

Answer 1

Đặt \(2^0+2^1+2^2+...+2^{2016}=A\)

\(A=2^0+2^1+2^2+...+2^{2016}\)

\(A=1+2+2^2+2^3+...+2^{2016}\)

\(2A=2+2^2+2^3+2^4+...+2^{2017}\)

\(2A-A=2+2^2+2^3+...+2^{2017}-1-2-2^2-2^3-...-2^{2016}\)

\(A=2^{2017}-1\)

\(=>2^{2017}-1< 2^{2017}\)

Answer 2

2²⁰¹⁷ lớn hơn so với 2⁰+2¹+2²+2³+2^4+...+2²⁰¹⁶