các phân số theo thứ tự từ bé đến lớn là: 1/12,5/12,14/13

1/12;5/12;14/13

\(\frac{1}{12}\); \(\frac{14}{13}\); \(\frac{5}{12}\)

\(\Rightarrow\frac{13}{156};\frac{168}{156};\frac{65}{156}\)

Vì \(\frac{13}{156}< \frac{65}{156}< \frac{168}{156}\)

nên \(\frac{1}{12}< \frac{5}{12}< \frac{14}{13}\)

= 128/256 + 64/256 + 32/256 + 16/256 + 8/256 + 4/256 + 2/256 + 1/256 

= 255/256

q​uy đ​ồ​ng mẫ​u số​ bạ​n nhé​. Mẫ​u số chung = 256

12+14+18+164+1128+1256" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:15.82px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-break:break-word; word-spacing:normal" class="MathJax_CHTML mjx-chtml">12+14+18+164+1128+1256" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:15.82px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-break:break-word; word-spacing:normal" class="MathJax_CHTML mjx-chtml">12+14+18+164+1128+1256

121+122+123+124+125+126+127+128" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:15.82px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-break:break-word; word-spacing:normal" class="MathJax_CHTML mjx-chtml">121+122+123+124+125+126+127+128

121+122+123+124+125+126+127+128)" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:15.82px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-break:break-word; word-spacing:normal" class="MathJax_CHTML mjx-chtml">121+122+123+124+125+126+127+128)

121+122+123+124+125+126+127" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:15.82px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-break:break-word; word-spacing:normal" class="MathJax_CHTML mjx-chtml">121+122+123+124+125+126+127

121+122+123+124+125+126+127)&#x2212;(121+122+123+124+125+126+127+128)" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-table; float:none; font-size:15.82px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-break:break-word; word-spacing:normal" class="MathJax_CHTML mjx-chtml">121+122+123+124+125+126+127)−(121+122+123+124+125+126+127+128)128=1&#x2212;1256=255256" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:15.82px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-break:break-word; word-spacing:normal" class="MathJax_CHTML mjx-chtml">A=1−128=1−1256=255256

    1/2    + 1/4     + 1/8  + 1/16  + 1/32 + 1/64

 = 32/64 + 16/64 + 8/64 + 4/64 + 2/64 + 1/64

 =                         63/64

Chúc bạn học tốt nha!^-^

=63nha ban

\(A=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+....+\frac{1}{256}-\frac{1}{512}\)

\(=\frac{1}{2}-\frac{1}{512}\)

\(=\frac{255}{512}\)

Vậy \(A=\frac{255}{512}\)

A=14 +18 +116 +132 +164 +1128 +1256 +1512 

=12 −14 +14 −18 +....+1256 −1512 

=12 −1512 

=255512 

Vậy A=255512 

Phạm Long Khánh

A = 255/512

1/ 2 + 2 = 4

2/ 4 + 4 = 8

3/ 8 + 8 = 16

4/ 16 + 16 = 32

5/ 32 + 32 =64

6/ 64 + 64 =128

7/ 128 + 128 =256

8/  256 + 256 =512

9/ 521 + 512 =1033

10/ 2048 + 2048 =4096

k mình đi

4

8

16

32

64

128

256

512

2048

4096

theo mình nghĩ là như th61 này

\(2\cdot2^{99}-2^{99}=2^{99}\)

\(2^{99}=2\cdot2^{98}\)

\(2\cdot2^{98}-2^{98}=2^{98}\)

vậy tức là \(2^n-2^{n-1}=2^{n-1}\)

đến cuối bạn sẽ có \(2^3-2^2=4\)

4-2-1=1

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

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 ..........

Ta có :

\(\frac{1}{101}>\frac{1}{200}\)

\(\frac{1}{102}>\frac{1}{200}\)

\(\frac{1}{103}>\frac{1}{200}\)

\(.........\)

\(\frac{1}{200}=\frac{1}{200}\)

Cộng vế với vế ta được :

\(\frac{1}{101}+\frac{1}{102}+.....+\frac{1}{200}>\frac{1}{200}+\frac{1}{200}+....+\frac{1}{200}\) (có 100 số hạng \(\frac{1}{200}\))\(=\frac{100}{200}=\frac{1}{2}\)

\(\Rightarrow\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+.....+\frac{1}{200}>\frac{1}{2}\)