Question

Tính nhanh tổng sau:

A=1+2+2²+2³+.........+2⁶⁴

Answer 1

\(A=1+2+2^2+2^3+...+2^{64}\)

\(2A=2+2^2+2^3+2^4+...+2^{64}+2^{65}\)

\(2A-A=\left(2+2^2+2^3+2^4+....+2^{64}+2^{65}\right)-\left(1+2+2^2+2^3+...+2^{64}\right)\)

\(2A-A=2+2^2+2^3+2^4+...+2^{64}+2^{65}-1-2-2^2-2^3-...-2^{64}\)

\(A=2^{65}-1\)

Answer 2

A=1+2+2²+2³+...+2⁶⁴

2A=2+2²+2³+2⁴+...+2⁶⁵

2A-A=2+2²+2³+2⁴+...+2⁶⁵-(1+2+2²+2³+...+2⁶⁴)

A=2⁶⁵-1