Question

[lương ngọc diễm]

1/2+1/4+1/8+1/16+...+1/512

1/2+1/6+ 1/12+ 1/20+1/30+.....1/90+ 1/110

trình bày cách làm hộ mình nha!

Answer 1

[Edogawa Conan]

Ta có:

\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^9}\)

\(\Rightarrow2A=2\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)=1+\frac{1}{2}+...+\frac{1}{2^8}\)

\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^8}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^9}\right)\)

\(\Rightarrow A=1-\frac{1}{2^9}=1-\frac{1}{512}=\frac{511}{512}\)

Vậy giá trị biểu thức là \(\frac{511}{512}\)

b) Ta có:

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}+\frac{1}{110}=\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{9.10}+\frac{1}{10.11}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)

\(=1-\frac{1}{11}=\frac{10}{11}\)

Vậy giá trị biểu thức là \(\frac{10}{11}\)

Answer 2

[lương ngọc diễm]

minh ko hiểu gi cả?