Question

Tính tổng A= 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 . Ai giúp mình bài này với nhá. 😁😁

Answer 1

Ta có:2A=\(2+1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)

2A-A=\(\left(2+1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)-\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)

\(=2-\frac{1}{32}=\frac{63}{32}=A\)

Answer 2

Ta có: \(A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

\(\Rightarrow A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}\)

\(\Rightarrow2A=2+1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}\)

\(\Rightarrow2A-A=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}\right)\)

\(\Rightarrow A=1-\frac{1}{2^5}=\frac{31}{32}\)

Vậy \(A=\frac{31}{32}\)

Answer 3

1/2=1- 1/2

1/4=1/2 -1/4

A=1+1-1/2+1/2-1/4+1/8-1/8+1/8-1/16+1/16-1/32

A=1+1-1/36

71/36

Answer 4

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

2A -A = 2-1/32 = 63 /32