The value of 1/ 2+1/ 3+ 1/ 4+ 1/5 is: (1) 5/46 (2) 68/157 (3) 157/68 (4) 21/110

Question

The value of \(\frac{1}{2+ \cfrac{1}{3+ \cfrac{1}{4 + \frac{1}{5}}}}\) is:

(1) \(\frac{5}{46}\)

(2) \(\frac{68}{157}\)

(3) \(\frac{157}{68}\)

(4) \(\frac{21}{110}\)

Answer 1

Correct option is: (2) \(\frac{68}{157}\)

\(\frac{1}{2 + \cfrac{1}{3+ \cfrac{1}{4 + \frac{1}{5}}}}\)

\(= \frac{1}{2 + \cfrac{1}{3 + \frac{1}{\frac{21}{5}}}}\)

\(= \frac{1}{2+ \cfrac{1}{3 + \frac{5}{21}}}\)

\(= \frac{1}{2 + \frac{1}{\frac{68}{21}}}\)

\(= \frac{1}{2 + \frac{21}{68}}\)

\(= \frac{1}{\frac{157}{68}}\)

\(= \frac{68}{157}\)