Question

Cho A = 1 + 2 + 2^2 + 2 ^ 3 + ... + 2 ^2017

va B -= 2^2018 - 1

So sanh A va B

giai ra giu mk nha

Answer 1

Ta có:\(A=1+2+2^2+2^3+....+2^{2017}.\)

\(\Rightarrow2A=2^1+2^2+2^3+2^4+....+2^{2018}\)

\(\Rightarrow2A-A=\left(2^1+2^2+2^3+2^4+...+2^{2018}\right)-\left(1+2^1+2^2+2^3+...+2^{2017}\right)\)

\(\Rightarrow A=2^{2018}-1\)

\(\Rightarrow A=B\)