Rút gọn biểu thức:

Question

2^100 - 2^99 + 2^98 -2^97 +...+ 2^2 - 2

Answer 1

2A = 2^101 -2^100 +2^99 - 2^98 + ..... + 2^3 - 2^2

2A + A = 2^101 -2^100 +2^99 - 2^98 + ..... + 2^3 - 2^2 + 2^100 - 2^99 + 2^98 -2^97 +...+ 2^2 - 2

3A= 2^101-2

A= (2^101 - 2)/3