Question
Download Solution PDF\( 2+\frac{1}{2-\frac{1}{3-\frac{1}{4-\frac{1}{4}}}}=?\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
We have,
\( 2+\frac{1}{2\ -\ \frac{1}{3\ -\ \frac{1}{4\ -\ \frac{1}{4}}}}\)
⇒ \( 2+\frac{1}{2\ -\ \frac{1}{3\ -\ \frac{1}{\frac{16\ -\ 1}{4}}}}\)
⇒ \( 2+\frac{1}{2\ -\ \frac{1}{3\ -\ \frac{4}{15}}}\)
⇒ \( 2+\frac{1}{2\ -\ \frac{1}{\frac{41}{15}}}\)
⇒ \( 2+\frac{1}{2\ -\ \frac{15}{41}}\)
⇒ \( 2+\frac{1}{\frac{67}{41}}\)
⇒ \( 2+\frac{41}{67}\)
⇒ \( 2\frac{41}{67}\)
∴ \( 2+\frac{1}{2\ -\ \frac{1}{3\ -\ \frac{1}{4\ -\ \frac{1}{4}}}}\) = \( 2\frac{41}{67}\)
Last updated on May 26, 2025
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