Question

tính

A= 1+ \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + ......+ \(\dfrac{1}{1024}\) giúp mk Quỳnh Phương Nguyễn Ace Legona Nguyễn Huy Tú

Answer 1

Ta có:

\(2A=2.\left(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{1024}\right)\)

\(=2.1+2.\dfrac{1}{2}+2.\dfrac{1}{4}+2.\dfrac{1}{8}+...+2.\dfrac{1}{1024}\)

\(=2+1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{512}\)

Ta lại có:

\(A=\left(2+1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{512}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{1024}\right)\)

\(=2-\dfrac{1}{1024}=\dfrac{2047}{1024}\)