Question

so sánh

1 + 2+2^2+2^3+......+2^30 và B = 23

Answer 1

Lời giải:

Ta có: \(A=1+2+2^2+...+2^{30}\)

\(\Rightarrow 2A=2+2^2+2^3+...+2^{30}+2^{31}\)

Trừ hai vế cho nhau:

\(2A-A=(2+2^2+2^3+...+2^{30}+2^{31})-(1+2+2^2+...+2^{30})\)

\(\Leftrightarrow A=2^{31}-1\)

Ta có: \(A=2^{31}-1>2^5-1\Leftrightarrow A>31>23\)

Hay \(A>B \)

Answer 2

Đặt \(A=1+2+2^2+2^3+..+2^{30}\)

\(2A=2\left(1+2+2^2+2^3+...+2^{30}\right)\)

\(2A=2+2^2+2^3+2^4+...+2^{31}\)

\(A=2A-A=\left(2+2^2+2^3+2^4+...+2^{31}\right)-\left(1+2+2^2+2^3+...+2^{30}\right)\)

\(A=2^{31}-1\)

Còn lại tự làm