\(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+...+\frac{1}{512}+\frac{1}{1024}=??????????\)

\(< =>1+\frac{1}{1\cdot2}+\frac{1}{2\cdot2}+\frac{1}{2\cdot4}+...+\frac{1}{2\cdot256}+\frac{1}{2\cdot512}\)

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

\(< =>1+\frac{1}{1}-\frac{1}{512}\)

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

chuc ban hoc tot nhe :))

#)Giải :

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

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+...+\frac{1}{256}-\frac{1}{512}\)

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

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

Lời giải 

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-\frac{1}{16}+...+\frac{1}{256}-\frac{1}{512}\)

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

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

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

A=1- bạn gạch chéo từ 1/2(đầu tiên) đến 1/32 nha

A=1-1/64=65/64.

B=Bạn làm tương tự như trên nha

k mik nha. Thanks. Chúc bạn học tốt!!!

a)  A=1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64

   2A=1+1/2+1/4 + 1/8 + 1/16 + 1/32 

  2A-A= 1+1/2+1/4+1/8+1/16+1/32-(1/2+1/4+1/8+1/16+1/32+1/64)

 A= 1-1/64=63/64

b) B= 1/4+1/8+1/16+......+1/512

2B= 1/2+1/4+1/8+1/16+......+1/256

2B-B=1/2+1/4+1/8+1/16+.....+1/256-(1/4+1/8+1/16+.....+1/512)

B=1/2-1/512=255/512

Ta có: \(\frac{1}{2}=1-\frac{1}{2}\);

\(\frac{1}{4}=\frac{1}{2}-\frac{1}{4}\); \(\frac{1}{8}=\frac{1}{4}-\frac{1}{8}\);...; \(\frac{1}{512}=\frac{1}{256}-\frac{1}{512}\); \(\frac{1}{1024}=\frac{1}{512}-\frac{1}{1024}\)

=> \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}+\frac{1}{1024}\)

=> \(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{256}-\frac{1}{512}+\frac{1}{512}-\frac{1}{1024}\)

=> \(A=1-\frac{1}{1024}=\frac{1023}{1024}\)

Đáp số: \(A=\frac{1023}{1024}\)

Dãy số đó có số số hạng là :

( 1/1024 - 1 ) : 

( 1 + 1/1024 ) * 

?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????/??bố thằng nào mà biết được

1/2 + 1/4+ 1/8+ 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512
= 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
= 1 – 1/512

= 511/512 .

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

Ta có : 
1/512 = 1×2 / 512×2 = 2/1024 

1/256 = 1×4 / 256×4 = 4/1024 

1/128 = 1×8 / 128×8 = 8/1024 

1/64 = 1×16 / 64×16 = 16/1024 

1/32 = 1×32 / 32×32 = 32/1024 

1/16 = 1×64 / 16×64 = 64/1024 

1/8 = 1×128 / 8×128 = 128/1024 

1/4 = 1×256 / 4×256 = 256/1024 

1/2 = 1×512 / 2×512 = 512/1024 
___________________________ 

=> 
1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024 

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

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

= 1023/1024 

255/256