Question

kết quả của dãy tính 1/2+1/4+1/8+1/16+...1/256+1/512 bằng..,

Answer 1

1/2 + 1/4 =3/4

1/2+1/4 +1/8=7/8

1/2+1/4+1/8+1/16=15/16

....tương tự ta có

1/2 +1/4+1/8+1/16+...+1/256+1/512=511/512

Answer 2

\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{256}+\frac{1}{512}\)

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

\(=\frac{511}{512}\)

Answer 3

Đặt \(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{256}+\frac{1}{512}\)

\(Ax2=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{256}\)

\(Ax2-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{256}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{256}+\frac{1}{512}\right)\)

\(A=1-\frac{1}{512}\)

\(A=\frac{511}{512}\)