Question

tính nhanh;

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

Answer 1

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

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

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

\(A=1-\frac{1}{32}=\frac{31}{32}\)

Answer 2

31/32 nhé bạn

Answer 3

=31/32 nhe ban !

Answer 4

31/32 nha!

Answer 5

31/32 

Answer 6

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

ta có:

1/2=1-1/2

1/4=1/2-1/4

1/8=1/4-1/8

.........

Cứ thế,ta có dãy tính:

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

=1-1/32

31/32

Answer 7

=31/32

Answer 8

31 / 32 nhabn 

Answer 9

31/32 là đúng cmn nha bạn

Answer 10

31/32 nha

t cho mình nha

Answer 11

Đặt biểu thức trên là A ta có

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

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

\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)

\(\Rightarrow A=1-\frac{1}{32}\)

    \(A=\frac{31}{32}\)

Answer 12

C1:\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

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

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

\(=\frac{31}{32}\)

C2: gọi \(S=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

\(\Leftrightarrow2S=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)

\(\Leftrightarrow2S-S=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)

\(\Leftrightarrow S=1-\frac{1}{32}=\frac{31}{32}\)

Answer 13

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

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

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

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

\(S=1-\frac{1}{32}\)

\(S=\frac{31}{32}\)

Answer 14

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

\(A=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^5}\)

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

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

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

Answer 15

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

\(2B=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\times2\)

\(2B=\frac{1}{2}\times2+\frac{1}{4}\times2+\frac{1}{8}\times2+\frac{1}{16}\times2+\frac{1}{32}\times2\)

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

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

\(B=1-\frac{1}{32}\)

\(B=\frac{31}{32}\)