Question:
Find the value of the expression: $1 – \frac{7}{1 – \frac{1}{1 + \frac{7}{1 – 7}}}$
व्यंजक का मान ज्ञात कीजिए: $1 – \frac{7}{1 – \frac{1}{1 + \frac{7}{1 – 7}}}$
Options:
- a) -1
- b) 2
- c) 1
- d) 0
- a) -1
- b) 2
- c) 1
- d) 0
correct answer : d)
Explanation:
We evaluate the continued fraction step-by-step starting from the bottom:
1. $1 – 7 = -6$
2. $1 + \frac{7}{1-7} = 1 + \frac{7}{-6} = 1 – \frac{7}{6} = -\frac{1}{6}$
3. $\frac{1}{1 + \frac{7}{1-7}} = \frac{1}{-1/6} = -6$
4. $1 – \frac{1}{1 + \frac{7}{1-7}} = 1 – (-6) = 7$
5. $\frac{7}{1 – \frac{1}{1 + \frac{7}{1-7}}} = \frac{7}{7} = 1$
6. $1 – 1 = 0$.
Hence, option (d) is the correct answer.
हम नीचे से शुरू करके चरण-दर-चरण सतत भिन्न का मूल्यांकन करते हैं:
1. $1 – 7 = -6$
2. $1 + \frac{7}{1-7} = 1 + \frac{7}{-6} = 1 – \frac{7}{6} = -\frac{1}{6}$
3. $\frac{1}{1 + \frac{7}{1-7}} = \frac{1}{-1/6} = -6$
4. $1 – \frac{1}{1 + \frac{7}{1-7}} = 1 – (-6) = 7$
5. $\frac{7}{1 – \frac{1}{1 + \frac{7}{1-7}}} = \frac{7}{7} = 1$
6. $1 – 1 = 0$।
अतः, विकल्प (d) सही उत्तर है।