Question

tính các biểu thức sau bằng 2 cách a,A=1/2+1/4+1/8+1/16+1/32+1/64

Answer 1

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

\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

\(\Rightarrow2A-A=1-\frac{1}{64}\)

\(\Rightarrow A=\frac{63}{64}\)

Answer 2

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+..+\frac{1}{32}-\frac{1}{64}\)

\(A=1-\frac{1}{64}\)

\(A=\frac{63}{64}\)Đây là cách 1

\(Ax2=1+\left(\frac{1}{2}+...+\frac{1}{64}\right)-\frac{1}{64}\)

\(Ax2=1+A-\frac{1}{64}\)

\(Ax2-A=1-\frac{1}{64}\)

\(A=\frac{63}{64}\)Đây là cách 2

Answer 3

P/s: Làm 1 cách đc kh???

A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64

2A = 1/2 x 2 + 1/4 x 2 + 1/8 x 2 + 1/16 x 2 + 1/32 x 2 + 1/64 x 2

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

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

A = 1 -  1/64

A = 63/64