Chứng minh rằng A = 1/2 - 2/2^2 + 3/2^3 - 4/2^4 + ...99/2^99 - 100/2^100 < 2/9

Chứng minh rằng

A=1/2 - 2/2^2 + 3/2^3 - 4/2^4 + ...99/2^99 - 100/2^100 < 2/9