Question

kết quả của dãy số 

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

các bn giúp mình nha

Answer 1

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

Answer 2

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 .

Answer 3

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

2A=\(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{256}\)

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

A=1-\(\frac{1}{512}\) =511/512