Question

Tính A=1/2+1/4+1/8+1/16+...{tổng của 10 số hạng}

Answer 1

a = 1/2+1/4+1/8+1/16

= (1 - 1/2) + (1/2 -1/4) + (1/4 - 1/8) + ... + (1/512 - 1/1024).

= 1 - 1/1024

= 1023/1024

ĐS 1023/1024

Duyệt đi

Answer 2

1023/1024

duyệt đi

Answer 3

Ta có : \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{1024}\)

\(\Rightarrow A=\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{10}}\)

\(\Rightarrow2A=2.\left(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{10}}\right)\)

\(\Rightarrow2A=1+\frac{1}{2^1}+\frac{1}{2^2}+....+\frac{1}{2^9}\)

\(\Rightarrow2A-A=\left(1+\frac{1}{2^1}+\frac{1}{2^2}+....+\frac{1}{2^9}\right)-\left(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{10}}\right)\)

\(\Rightarrow A=1-\frac{1}{2^{10}}=1-\frac{1}{1024}=\frac{1023}{1024}\)

Answer 4

a = 1/2+1/4+1/8+1/16

= (1 - 1/2) + (1/2 -1/4) + (1/4 - 1/8) + ... + (1/512 - 1/1024).

= 1 - 1/1024

= 1023/1024

ĐS 1023/1024

Answer 5

Dãy số hoàn chỉnh là :

\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}+\frac{1}{1024}\)

= \(1-\frac{1}{1024}\)

= \(\frac{1023}{1024}\)