Question

K=(1-\(\frac{1}{2}\))+(1-\(\frac{1}{4}\))+(1-\(\frac{1}{8}\))+...+(1-\(\frac{1}{1024}\))

(Dấu trừ viết hơi nhỏ)

 

Answer 1

\(K=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{8}\right)+...+\left(1-\frac{1}{1024}\right)\)

\(K=\left(1-\frac{1}{2^1}\right)+\left(1-\frac{1}{2^2}\right)+\left(1-\frac{1}{2^3}\right)+...+\left(1-\frac{1}{2^{10}}\right)\)

\(K=\left(1+1+1+...+1\right)-\left(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)\)

                 10 số 1                                         

\(K=10-\left(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)\)

                                     Đặt B

\(B=\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)

\(2B=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)

\(2B-B=1-\frac{1}{2^{10}}\)

\(B=1-\frac{1}{1024}=\frac{1023}{1024}\)

\(K=10-\frac{1023}{1024}=\frac{9217}{1024}\)

Số to wa ak

Answer 2

\(K=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{8}\right)+...+\left(1-\frac{1}{1024}\right)\)

\(K=\left(1+1+1+...+1\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{1024}\right)\)    

\(K=10-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{1024}\right)\)

\(2K=20-\left(1+\frac{1}{2}+\frac{1}{4}+....+\frac{1}{512}\right)\)