Đặt \(S=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{96}+\dfrac{1}{192}\)
\(\Rightarrow3S=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}\)
\(\Rightarrow6S=2+1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}\)
\(\Rightarrow6S-3S=2-\dfrac{1}{64}\)
\(\Rightarrow3S=\dfrac{127}{64}\)
\(\Rightarrow S=\dfrac{127}{192}\)
\(=\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{12}+...+\dfrac{1}{96}-\dfrac{1}{192}\\ =\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{192}\\ =\dfrac{127}{192}\)
ta có:
A=nhân tử của 2 vế với 6
/3+1/6+1/12+1/24+1/48+1/96-1/3-1/6+1/12-1/24-1/48-1/96-1/192
6xA-A=6-1/192
