Cộng thêm 1/2 vào biểu thức đã cho, có:

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

Nhận xét:

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

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

=0.99609375

cách 1 đó

2

4

8

16

32

64

128

256

2

4

8

16

64

128

256

          k mk nhé

1+1=2

2+2=4

4+4=8

8+8=16

16+16=32

32+32=64

64+64=128

128+128=256

tk m nhé

X x (1/2+1/4+1/8+1/16+1/32+1/64+1/128) = 127/128

X x 127/128                                            = 127/128

                                                        X   = 127/128 : 127/128

                                                        X   = 1

1+1=2

2+2=4

4+4=8

8+8=16

16+16=32

32+32=64

64+64=128

128+128=256

2

4

8

16

32

64

128

256

1+1=2

2+2=44+4=8

8+8=16

16+16=32

32+32=64

64+64=128

128+128=256

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

\(=\frac{4+2+1}{16}+\frac{4+2+1}{128}\)

\(=\frac{7}{16}+\frac{7}{128}\)

\(=\frac{56+7}{128}\)

\(=\frac{63}{128}\)

Nhớ k cho mình với nhé!

A = 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128

A x 2 = 1/4 - ( 1/4 + 1/8 + 1/16 + .............. + 1/64 + 1/128 ) - 1/128

A x 2 = 1/4 - A - 1/128

A x 2 - A = 1/4 - 1/128

A = 1/4 - 1/128

A = 31/128

A = 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128

A x 2 = 1/4 - ( 1/4 + 1/8 + 1/16 + .............. + 1/64 + 1/128 ) - 1/128

A x 2 = 1/4 - A - 1/128

A x 2 - A = 1/4 - 1/128

A = 1/4 - 1/128

A = 31/128

\(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}=\frac{32+16+8+4+2+1}{128}=\frac{63}{128}\)

Đặt A=1/4+1/8+1/16+1/32+1/64+1/128.

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

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

\(2A=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^6}\)

\(2A-A=\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^6}\right)-\left(\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^7}\right)\)

\(A=\frac{1}{2}-\frac{1}{2^7}\)

A=1/4+1/8+1/16+1/32+1/64+1/128

Ax2-A=(1/4+1/8+1/16+1/32+1/64+1/128)x2-(1/4+1/8+1/16+1/32+1/64+1/128)

Ax2-A=(1/2+1/4+1/8+1/16+1/32+1/64)-(1/4+1/8+1/16+1/32+1/64+1/128)

Ax2-A=1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64+1/64-1/128

A=1/2-1/128

A=    63/128.