Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Theo đề bài ta có :
\(2B=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{128}\)
\(\Leftrightarrow2B-B=\left(1+\frac{1}{2}+...+\frac{1}{128}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{256}\right)\)
\(\Leftrightarrow B=1-\frac{1}{256}\)
\(\Leftrightarrow B=\frac{255}{256}\)
\(B=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+..+\frac{1}{256}\)
\(\Rightarrow B=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+..+\frac{1}{2^8}\)
\(\Rightarrow2B=1+\frac{1}{2}+\frac{1}{2^2}+..+\frac{1}{2^7}\)
\(\Rightarrow2B-B=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^7}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^8}\right)\)
\(\Rightarrow B=1-\frac{1}{2^8}\)
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\)
=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{128}-\frac{1}{256}\)
=\(1-\frac{1}{256}\)
=\(\frac{255}{256}\)
1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256
= 128/256 + 64/256 + 32/256 + 16/256 + 8/256 + 4/256 + 2/128 + 1/256
= 255/256
Nhận xét :
1/2 = 1 - 1/2 ; 1/4 = 1/2 - 1/4 ; 1/8 = 1/4 - 1/8 ; ..... ; 1/256 = 1/128 - 1/256
=> A = 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + ..... + 1/128 - 1/256
=> A = 1 - 1/256 = 255/256
quy đồngcác phân số lấy mẫu số là 512 .ta có tử số là
256 +128 + 64 +32 +16 +8 +4 +2 +1 =495
A =\(\frac{495}{512}\)
Bài làm:
Đặt \(A=\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}=\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^8}\)
=> \(2A=\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^7}\)
=> \(2A-A=\left(\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^7}\right)-\left(\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^8}\right)\)
<=> \(A=\frac{1}{2^2}-\frac{1}{2^8}=\frac{2^6-1}{2^8}=\frac{64-1}{256}=\frac{63}{256}\)
đáp án là 63/256 nha bạn ~ mk hơi bận nên k kịp trình bày!
= (64/256 + 32/256 + 16/256 + 8/256 + 4/256 + 2/256) X x =1
= 126 X x = 1
x = 1 : 126
x= 1/126
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!
Đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)
\(2A=2.\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\right)\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(\Rightarrow2A-A=\left(1+\frac{1}{2}+.......+\frac{1}{64}+\frac{1}{128}\right)-\left(\frac{1}{2}+\frac{1}{4}+......+\frac{1}{128}+\frac{1}{256}\right)\)
\(\Rightarrow A=1-\frac{1}{256}\)
\(\Rightarrow A=\frac{255}{256}\)
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)
\(=\frac{128}{256}+\frac{64}{256}+\frac{32}{256}+\frac{16}{256}+\frac{8}{256}+\frac{4}{256}+\frac{2}{256}+\frac{1}{256}\)
\(=\frac{\left(128+2\right)+\left(64+16\right)+\left(32+8\right)+\left(4+1\right)}{256}\)
\(=\frac{130+80+40+5}{256}\)
\(=\frac{255}{256}\)
\(A=\frac{1}{2}+\frac{1}{4}+...+\frac{1}{256}\)
\(\Rightarrow2A=1+\frac{1}{2}+...+\frac{1}{128}\)
\(\Rightarrow A=2A-A=1-\frac{1}{256}\)
\(\Rightarrow A=\frac{255}{256}\)
Đặt:\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\)
\(\Rightarrow A=\frac{1}{2^1}+\frac{1}{2^2}+....+\frac{1}{2^8}\)
\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^7}\)
\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+..+\frac{1}{2^7}\right)-\left(\frac{1}{2^1}+\frac{1}{2^2}+...+\frac{1}{2^7}\right)\)
\(\Rightarrow A=1-\frac{1}{2^7}\)
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)\(+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)
= \(\left(\frac{1}{2}+\frac{1}{8}\right)+\left(\frac{1}{4}+\frac{1}{16}\right)+\left(\frac{1}{32}+\frac{1}{64}\right)\)\(+\left(\frac{1}{128}+\frac{1}{256}\right)\)
= \(\left(\frac{4}{8}+\frac{1}{8}\right)+\left(\frac{4}{16}+\frac{1}{16}\right)+\left(\frac{2}{64}+\frac{1}{64}\right)\) \(+\left(\frac{2}{256}+\frac{1}{256}\right)\)
= \(\frac{5}{8}+\frac{5}{16}+\frac{3}{64}+\frac{3}{256}\)
= \(\frac{160}{256}+\frac{80}{256}+\frac{12}{256}+\frac{3}{256}\)
= \(\frac{255}{256}\)
^^ Ủng hộ nha!
1 - 1/256 = \(\frac{255}{256}\)
Kết quả đấy mình thử lại đúng luôn
=(1-\(\frac{1}{2}\))+(\(\frac{1}{2}\)-\(\frac{1}{4}\))+(\(\frac{1}{4}\)-\(\frac{1}{8}\))+....+(\(\frac{1}{128}\)\(\frac{1}{256}\))
=1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{4}\)+\(\frac{1}{4}\)-\(\frac{1}{8}\)+....+\(\frac{1}{128}\)-\(\frac{1}{256}\)
=1-\(\frac{1}{256}\)=\(\frac{255}{256}\)
chuẩn 10000000000000% k cho mình nhé
Đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)
\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}+\frac{1}{2^8}\)
\(2A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}\)
\(\Rightarrow2A-A=1-\frac{1}{2^8}=\frac{255}{256}\)
\(\Rightarrow A=\frac{255}{256}\)
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)
\(2A=\frac{1}{2}\times2+\frac{1}{4}\times2+\frac{1}{8}\times2+\frac{1}{16}\times2+...+\frac{1}{256}\times2\)
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\right)\)
\(A=1-\frac{1}{256}\)
\(A=\frac{255}{256}\)
\(B=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\)
\(2B=1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{128}\)
\(2B-B=\left(1+\frac{1}{2}+...+\frac{1}{128}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{256}\right)\)
\(2B-B=1-\frac{1}{256}\)
\(B=\frac{255}{256}\)
=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
=1-1/256
=1
255/256
Trl
Bạn kia trả lời đúng rồi nhoa !
Hok tốt
~ NHÉ BẠN ~