Question

Chứng minh \(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}<\frac{1}{3}\)

Answer 1

Đặt A= 1/2-1/4+1/8-1/16+1/32-1/64

ta có 2A=1-1/2+1/4-1/8+1/16-1/32

2A-A=A=1-1/64=63/64

vì 63/64<1/3

=>A<1/3 (đpcm)

Answer 2

Ta thấy:

1/2-1/4+1/8-1/16+1/32-1/64 =

(1/2+1/4+1/8+1/16+1/32+1/64) – 2 x (1/4 + 1/16 + 1/64) =

(1 – 1/64) – 42/64 =

63/64 – 42/64 = 21/64 < 21/63=1/3

=>   1/2-1/4+1/8-1/16+1/32-1/64 < 1/3

Answer 3

=\(\frac{1}{2}+\frac{1}{8}+\frac{1}{32}=\frac{21}{32}>\frac{1}{3}\Rightarrow\)de bai sai