\(A=\frac{1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}}{1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}}\)
Đặt tử số là B, mẫu số là C
\(B=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
\(2B=2+1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\)
\(2B-B=\left(2+1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\right)-\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)\)
\(B=2-\frac{1}{16}\)
\(B=\frac{32}{16}-\frac{1}{16}=\frac{31}{16}\)
\(C=1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}\)
\(2C=2-1+\frac{1}{2}-\frac{1}{4}+\frac{1}{8}\)
\(2C+C=\left(2-1+\frac{1}{2}-\frac{1}{4}+\frac{1}{8}\right)+\left(1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}\right)\)
\(3C=2+\frac{1}{16}\)
\(3C=\frac{32}{16}+\frac{1}{16}\)
\(3C=\frac{33}{16}\)
\(C=\frac{33}{16}:3=\frac{11}{16}\)
=> \(A=\frac{B}{C}=\frac{31}{16}:\frac{11}{16}=\frac{31}{16}.\frac{16}{11}=\frac{31}{11}\)
