0,856m=?m

\(...=\dfrac{3}{2}x\left(1+\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+\dfrac{1}{256}\right)\)

\(=\dfrac{3}{2}x\left(\dfrac{256}{256}+\dfrac{64}{256}+\dfrac{16}{256}+\dfrac{4}{256}+\dfrac{1}{256}\right)\)

\(=\dfrac{3}{2}x\dfrac{341}{256}=\dfrac{1023}{512}\)

Đặt tổng trên là: \(A\)

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

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

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

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

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

3/512 là gì vậy bn?

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

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

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

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

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

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

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

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

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

Đinh Thùy LinhTính nhanh mà bạn cách này mk nhanh hơn nhiều :D

b: A=1/3+1/9+...+1/3^10

=>3A=1+1/3+...+1/3^9

=>A*2=1-1/3^10=(3^10-1)/3^10

=>A=(3^10-1)/(2*3^10)

c: C=3/2+3/8+3/32+3/128+3/512

=>4C=6+3/2+...+3/128

=>3C=6-3/512

=>C=1023/512

d: A=1/2+...+1/256

=>2A=1+1/2+...+1/128

=>A=1-1/256=255/256

Đặt A=3/2+3/8+...+3/512

bn tách

3/2=3/2^1

3/8=3/2^3

....

3/512=3/2^9

Rồi nhân nó lên trừ đc bao nhiêu - đi A ban đầu là đc

b:3=1/2+1/4+1/8+1/16+1/32+1/64+1/128

[b:3]x2=1+1/2+1/4+1/8+1/16+1/32+1/64

[b:3]x2-[b:3]=1+1/2+1/4+1/8+1/16+1/32+1/64-1/2+1/4+1/8+1/16+1/32+1/64+1/128

b:3=1-1/128

b:3=127/128

b=127/128x3

b=381/128

B.2=\(3+\frac{3}{2}+\frac{3}{4}+\frac{3}{8}+\frac{3}{16}+\frac{3}{32}+\frac{3}{64}\)\(+\frac{3}{128}\)

B.2-B=\(\left(3+\frac{3}{2}+\frac{3}{4}+\frac{3}{8}+\frac{3}{16}+\frac{3}{32}+\frac{3}{64}+\frac{3}{128}\right)\).\(\left(\frac{3}{2}+\frac{3}{4}+\frac{3}{8}+\frac{3}{16}+\frac{3}{32}+\frac{3}{64}+\frac{3}{128}\right)\)

B=3-\(\frac{3}{128}\)

B=\(\frac{381}{128}\)

b:3=1/2+1/4+1/8+1/16+1/32+1/64+1/128

[b:3]x2=1+1/2+1/4+1/8+1/16+1/32+1/64

[b:3]x2-[b:3]=1+1/2+1/4+1/8+1/16+1/32+1/64-1/2+1/4+1/8+1/16+1/32+1/64+1/128

b:3=1-1/128

b:3=127/128

b=127/128x3

b=381/128

cho mình 

3(1/2+1/4+1/8+1/16.....1/128)

A=(1/2+1/4+1/8+1/16....1/128)

2A-A=A

2A=(1/2+1/4+1/8....1/128)*2

=1+1/2+1/4....1/64

2A-A=1+1/2+1/4+1/8....1/64-(1/2+1/4+1/8......1/128)

A=1-1/128=127/128

Đáp số:3*127/128=381/128