K
Khách

Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.

17 tháng 7 2017

\(\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}\)

\(=\left(\frac{12}{8}+\frac{3}{8}\right)+\left(\frac{12}{128}+\frac{3}{128}\right)+\frac{3}{512}\)

\(=\frac{15}{8}+\frac{15}{128}+\frac{3}{512}\)

\(=\frac{240}{128}+\frac{15}{128}+\frac{3}{512}\)

\(=\frac{255}{128}+\frac{3}{512}\)

\(=\frac{1020}{512}+\frac{3}{512}\)

\(=\frac{1023}{512}\)

17 tháng 7 2017

\(\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}=\frac{3}{1.2}+\frac{3}{2.4}+\frac{3}{4.8}+\frac{3}{8.16}+\frac{3}{16.32}\)
                                                        \(=\frac{3}{1}-\frac{3}{2}+\frac{3}{2}-\frac{3}{4}+\frac{3}{8}-\frac{3}{8}+\frac{3}{16}-\frac{3}{16}+\frac{3}{32}\)
                                                         \(=3+\frac{3}{32}=\frac{3.32}{32}+\frac{3}{32}=\frac{96+3}{32}=\frac{99}{32}\)

\(\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}\)

\(=3.\left(\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}+\frac{1}{2^9}\right)\)

\(=3.A\)với \(A=\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}+\frac{1}{2^9}\)

\(\Rightarrow2^2A=\left(2+\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}\right)\)

\(\Rightarrow2^2A-A=\left(2+\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}\right)-\left(\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}+\frac{1}{2^9}\right)\)

\(\Rightarrow4A-A=2-\frac{1}{2^9}\)

\(\Rightarrow3A=2-\frac{1}{512}=\frac{1023}{512}\Rightarrow A=\frac{1023}{512}:3\)

\(\Rightarrow\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{3}{512}=3.\left(\frac{1023}{512}:3\right)=\frac{1023}{512}\)

24 tháng 8 2023

Đặt tổng trên là: \(A\)

\(A=\dfrac{3}{2}+\dfrac{3}{8}+\dfrac{3}{32}+\dfrac{3}{128}+\dfrac{3}{512}\)

\(\Rightarrow A.4=6+\dfrac{3}{2}+\dfrac{3}{8}+\dfrac{3}{32}+\dfrac{3}{128}\)

\(\Rightarrow A.4-A=\left(6+\dfrac{3}{2}+\dfrac{3}{8}+\dfrac{3}{32}+\dfrac{3}{128}\right)-\left(\dfrac{3}{2}+\dfrac{3}{8}+\dfrac{3}{32}+\dfrac{3}{128}+\dfrac{3}{512}\right)\)

\(\Rightarrow A.3=6-\dfrac{3}{512}=\dfrac{3069}{512}\)

\(\Rightarrow A=\dfrac{3069}{512}:3=\dfrac{1023}{512}\)

24 tháng 8 2023

3/512 là gì vậy bn?

 

20 tháng 3 2020

(3/2+3/8) +( 3/4 =3/16) +( 3/32+ 3/128)+(3,64+3,256)+3/512

= 4+6/2+6/16+6/896+3/512

=10/2+13/056+3/512

=23/256+3/512

=26/768

1+2+4+8+16+32+64+128+256+512+1024+2048

=1+(2+8)+(4+16)+(32+128)+(64+256)+(512+2048)+1024

=1+10+20+160+320+2560+1024

=4095

5 tháng 1 2017

 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 = 4095 

k nha      công chúa nụ cười    =_=   ^_^

24 tháng 6 2016

\(P+\frac{1}{512}=\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{3}{128}+\frac{4}{512}=\frac{3}{2}+\frac{3}{8}+\frac{3}{32}+\frac{4}{128}=\)

\(=\frac{3}{2}+\frac{3}{8}+\frac{4}{32}=\frac{3}{2}+\frac{4}{8}=\frac{4}{2}=2\)

\(\Rightarrow P=2-\frac{1}{512}=\frac{1023}{512}\)

24 tháng 6 2016

\(P=\frac{3}{2}+\frac{3}{8}+...+\frac{3}{512}\)

\(=3.\left(\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}+\frac{1}{2^9}\right)\)

\(4P=3\left(\frac{1}{2^3}+\frac{1}{2^5}+...+\frac{1}{2^{11}}\right)\)

\(4P-P=3\left(\frac{1}{2}-\frac{1}{2^{11}}\right)\)

\(3P=3\left(\frac{1}{2}-\frac{1}{2^{11}}\right)\)

\(P=\frac{1}{2}-\frac{1}{2^{11}}=\frac{2^{10}-1}{2^{11}}\)

20 tháng 6 2018

= (11+9+2)+(1/2-3/2+5/2)-(2/3+5/3-7/3)

=22+1,5-0

=23.5

24 tháng 2 2023

=(11+9+2)+(1/2-3/2+5/2)-(2/3+5/3-7/3)

=22+1,5-0

=23.5

Chúc học tốt

24 tháng 6 2016

P= 3/2 + 3/8 + 3/32 + 3/128 + 3/512

  = 768/512 + 192/512 + 48/512 + 12/512 + 3/512

  =1023/512

24 tháng 6 2016

1023 / 512