tính tổng dưới đây bằng cách nhanh nhất:
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1204
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Những câu hỏi liên quan
CP
1
TH
3
14 tháng 7 2016
1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
A x 2 = 1/4 ( 1/4 + 1/8 + 1/16 + .......... + 1/512 ) - 1/512
A x 2 = 1/4 - A - 1/512
A x 2 - A = 1/4 - 1/512
A = 1/4 - 1/512
A = 127/512
14 tháng 7 2016
1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
= 1/2 - 1/4 + 1/4 - 1/8 + ... + 1/256 - 1/512
= 1/2 - 1/512
= 255/512
TP
3
1 tháng 8 2016
A = 1/2 + 1/4 + 1/8 + ... + 1/1024
2A = 1 + 1/2 + 1/4 + ... + 1/512
2A - A = (1 + 1/2 + 1/4 + ... + 1/512) - (1/2 + 1/4 + 1/8 + ... + 1/1024)
A = 1 - 1/1024
A = 1023/1024
1 tháng 8 2016
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{1024}\)
\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{4}+......+\frac{1}{512}\)
\(\Rightarrow A=2A-A=1-\frac{1}{1024}\)
\(A=\frac{1023}{1024}\)
TT
2
3 tháng 8 2023
Đặt A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
=> 2A = 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128
=> 2A - A = (1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128) - (1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256)
=> A = 1 - 1/256
=> A = 255/256
Vậy: ...
TB
2
MC
7 tháng 8 2021
1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
= 1/2 - 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + ... + 1/256 - 1/512
= 1/2 - 1/512
= 255/512
NH
7 tháng 8 2021
Gọi \(\frac{1}{4}+\frac{1}{8}+\frac{1}{6}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\) là A
Ta có :
\(A=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\)
\(2A=2.\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\right)\)
\(2A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)
\(2A-A=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\right)-\left(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{11}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\right)\)
\(A=\frac{1}{2}-\frac{1}{512}\)
\(A=\frac{255}{512}\)
Vậy ..........
A
2
T
6 tháng 7 2019
#)Giải :
\(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\)
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+...+\frac{1}{256}-\frac{1}{512}\)
\(=\frac{1}{2}-\frac{1}{512}\)
\(=\frac{255}{512}\)
6 tháng 7 2019
Lời giải
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+...+\frac{1}{256}-\frac{1}{512}\)
\(=\frac{1}{2}-\frac{1}{512}\)
\(=\frac{255}{512}\)
TD
4
8 tháng 4 2016
A= 1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
A = 1 - 1/2 + 1/2- 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 - 1/32 + 1/32 - 1/64 + 1/64 - 1/128 + 1/128 - 1/256 - 1/256 - 1/512
A = 1 - 1/512
A = 511/512
Chúc bạn học giỏi nha!
8 tháng 4 2016
gọi biểu thức đó là A
A=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512
1/512+A=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/512
1/512+A=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/256
1/512+A=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/128
1/512+A=1/2+1/4+1/8+1/16+1/32+1/64+1/64
1/512+A=1/2+1/4+1/8+1/16+1/32+1/32
1/512+A=1/2+1/4+1/8+1/16+1/16
1/512+A=1/2+1/4+1/8+1/8
1/512+A=1/2+1/4+1/4
1/512+A=1/2+1/2
1/512+A=1
A=1-1/512
A=511/512
chắc 100%
20 tháng 2 2020
\(\frac{3}{2}+\frac{3}{4}+\frac{3}{8}+\frac{3}{16}+\frac{3}{32}+\frac{3}{64}+\frac{3}{128}+\frac{3}{256}+\frac{3}{512}+\frac{3}{1024}\)
=\(3.\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}+\frac{1}{1024}\right)\)
=\(3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+\frac{1}{16}-\frac{1}{32}+\frac{1}{32}-\frac{1}{64}+\frac{1}{64}-\frac{1}{128}+\frac{1}{128}-\frac{1}{256}+\frac{1}{256}-\frac{1}{512}+\frac{1}{512}-\frac{1}{1024}\right)\)
=\(3.\left(1-\frac{1}{1024}\right)=3.\left(\frac{1024}{1024}-\frac{1}{1024}\right)=3.\frac{1023}{1024}=\frac{3069}{1024}\)
Chúc em học tốt
bằng 511/512