Question:
Find the value of the continued fraction shown in the image.
चित्र में दिखाई गई सतत भिन्न (continued fraction) का मान ज्ञात कीजिए।
Options:
- a) 2 11/45
- b) 1 38/45
- c) 2 17/45
- d) 1 13/45
- a) 2 11/45
- b) 1 38/45
- c) 2 17/45
- d) 1 13/45
correct answer : b)
Explanation:
Evaluating the continued fraction from the bottom: 1) 2 + 1/3 = 7/3. 2) 5 + 1/(7/3) = 5 + 3/7 = 38/7. 3) 1 + 1/(38/7) = 1 + 7/38 = 45/38. 4) 1 + 1/(45/38) = 1 + 38/45 = 83/45 = 1 38/45.
नीचे से सतत भिन्न का मान ज्ञात करने पर: 1) 2 + 1/3 = 7/3। 2) 5 + 1/(7/3) = 5 + 3/7 = 38/7। 3) 1 + 1/(38/7) = 1 + 7/38 = 45/38। 4) 1 + 1/(45/38) = 1 + 38/45 = 83/45 = 1 38/45।