a, \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+....+\frac{1}{10100}\)

=\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{100.101}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{100}-\frac{1}{101}\)

=\(1-\frac{1}{101}\)

=\(\frac{100}{101}\)

b,\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{512}\)

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

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

=\(\frac{511}{512}\)

\(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{9900}+\frac{1}{10100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}+\frac{1}{100}-\frac{1}{101}\)

\(=1-\frac{1}{101}=\frac{100}{101}\)

a) trieu dang làm rồi

b)   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

Đặt A=1/2+1/4+1/6+1/8+1/16+...+1/256+1/512

=(1/2+1/4+1/8+1/16+...+1/256+1/256-1/512)+1/6

=(1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+...+1/128-1/256+1/256-1/512)+1/6

=1-1/512+1/6

=1789/1536

Vậy A=1789/1536

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

hok tot

chỗ k ở đâu để mình k cho

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 

Đặt \(A=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}+\dfrac{1}{512}\)

\(\Rightarrow2A=1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{128}+\dfrac{1}{256}\)

\(\Rightarrow A=2A-A=1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{128}+\dfrac{1}{256}-\dfrac{1}{2}-\dfrac{1}{4}-\dfrac{1}{8}-...-\dfrac{1}{256}-\dfrac{1}{512}\)

\(\Rightarrow A=1-\dfrac{1}{512}=\dfrac{511}{512}\)

Đặt 

1/2 + 1/4 + 1/8 + 1/16 + ... + 1/256 + 1/512

= 256/512 + 128/512 + 64/512 + ... + 2/512 + 1/512

= 256 + 128 + 64 + .. + 2 + 1 / 512

= ???????

s=1/2+1/4+1/8+1/16+.....+1/256+1/512

sx2=(1/2+1/4+1/8+1/16+....+1/256+1/512)x2

sx2=1+1/2+1/4+1/8+......+1/126+1/256

sx2-s=(1+1/2+1/4+1/8+......+1/256)-(1/2+1/4+1/8+1/16++.....+1/256+1/512)

1+1/2+1/4+1/8+......+1/256-1/2-1/4-1/8-1/16-.....1/256-1/512

=1-1/512=511/512

Vậy dãy số đó là:

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

256/512 + 128/512 + 64/512 + 32/512 + 16/512 + 8/512 + 4/512 + 2/512 + 1/512 511/512

Đáp số: 511/512