1/2+1/4/1/6+1/8+1/10+1/12+1/14+1/16+1/18+1/20+1/22

asked by guest
on Sep 24, 2024 at 1:31 pm



You asked:

Evaluate the expression: \(\frac{1}{2} + \frac{\frac{\frac{1}{4}}{1}}{6} + \frac{1}{8} + \frac{1}{10} + \frac{1}{12} + \frac{1}{14} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \frac{1}{22}\)

MathBot Answer:

\[\frac{1}{2} + \frac{\frac{\frac{1}{4}}{1}}{6} + \frac{1}{8} + \frac{1}{10} + \frac{1}{12} + \frac{1}{14} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \frac{1}{22} = \frac{62921}{55440} = 1.1349\overline{386724}\]

\[\begin{aligned}\frac{1}{2} + \frac{\frac{\frac{1}{4}}{1}}{6} + \frac{1}{8} + \frac{1}{10} + \frac{1}{12} + \frac{1}{14} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \frac{1}{22}& = \frac{1}{2} + \frac{1}{4} \cdot 1^{-1} \cdot \frac{1}{6} + \frac{1}{8} + \frac{1}{10} + \frac{1}{12} + \frac{1}{14} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \frac{1}{22}\\& = \frac{1}{2} + \frac{1}{4} \cdot \frac{1}{6} + \frac{1}{8} + \frac{1}{10} + \frac{1}{12} + \frac{1}{14} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \frac{1}{22}\\& = \frac{1}{2} + \frac{1}{24} + \frac{1}{8} + \frac{1}{10} + \frac{1}{12} + \frac{1}{14} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \frac{1}{22}\\& = \frac{13}{24} + \frac{1}{8} + \frac{1}{10} + \frac{1}{12} + \frac{1}{14} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \frac{1}{22}\\& = \frac{2}{3} + \frac{1}{10} + \frac{1}{12} + \frac{1}{14} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \frac{1}{22}\\& = \frac{23}{30} + \frac{1}{12} + \frac{1}{14} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \frac{1}{22}\\& = \frac{17}{20} + \frac{1}{14} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \frac{1}{22}\\& = \frac{129}{140} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \frac{1}{22}\\& = \frac{551}{560} + \frac{1}{18} + \frac{1}{20} + \frac{1}{22}\\& = \frac{5239}{5040} + \frac{1}{20} + \frac{1}{22}\\& = \frac{5491}{5040} + \frac{1}{22}\\& = \frac{62921}{55440}\end{aligned}\]

+ Submit Question