Toán Chứng minh rằng 1/2-1/4+1/8-1/16+1/32-1/64<1/3 13/10/2021 By Kaylee Chứng minh rằng 1/2-1/4+1/8-1/16+1/32-1/64<1/3
Đặt A= $\frac{1}{2}$- $\frac{1}{4}$+ $\frac{1}{8}$- $\frac{1}{16}$+ $\frac{1}{32}$- $\frac{1}{64}$ 2A= 1- $\frac{1}{2}$- $\frac{1}{4}$+ $\frac{1}{8}$- $\frac{1}{16}$+ $\frac{1}{32}$ 2A- A= 1- $\frac{1}{64}$ A= $\frac{63}{64}$ Vì $\frac{63}{64}$< $\frac{1}{3}$ nên $\frac{1}{2}$- $\frac{1}{4}$+ $\frac{1}{8}$- $\frac{1}{16}$+ $\frac{1}{32}$- $\frac{1}{64}$< 3 Vậy $\frac{1}{2}$- $\frac{1}{4}$+ $\frac{1}{8}$- $\frac{1}{16}$+ $\frac{1}{32}$- $\frac{1}{64}$< 3 CHO MIK CTLHN NHÉ Trả lời
1/2-1/4+1/8-1/16+1/32-1/64 =(1/2-1/4)+(1/8-1/16)+(1/32-1/64) =1/4+1/16+1/64 =21/64 mà 21/64 <21/63=1/3 vậy 1/2-1/4+1/8-1/16+1/32-1/64<1/3 Trả lời
Đặt A= $\frac{1}{2}$- $\frac{1}{4}$+ $\frac{1}{8}$- $\frac{1}{16}$+ $\frac{1}{32}$- $\frac{1}{64}$
2A= 1- $\frac{1}{2}$- $\frac{1}{4}$+ $\frac{1}{8}$- $\frac{1}{16}$+ $\frac{1}{32}$
2A- A= 1- $\frac{1}{64}$
A= $\frac{63}{64}$
Vì $\frac{63}{64}$< $\frac{1}{3}$
nên $\frac{1}{2}$- $\frac{1}{4}$+ $\frac{1}{8}$- $\frac{1}{16}$+ $\frac{1}{32}$- $\frac{1}{64}$< 3
Vậy $\frac{1}{2}$- $\frac{1}{4}$+ $\frac{1}{8}$- $\frac{1}{16}$+ $\frac{1}{32}$- $\frac{1}{64}$< 3
CHO MIK CTLHN NHÉ
1/2-1/4+1/8-1/16+1/32-1/64
=(1/2-1/4)+(1/8-1/16)+(1/32-1/64)
=1/4+1/16+1/64
=21/64
mà 21/64 <21/63=1/3
vậy 1/2-1/4+1/8-1/16+1/32-1/64<1/3