Question
Download Solution PDF\(1+\frac{1}{1+\frac{1}{5+\frac{1}{2+\frac{1}{3}}}}\) এর মান কত?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত:
অভিব্যক্তি: \(1+\frac{1}{1+\frac{1}{5+\frac{1}{2+\frac{1}{3}}}}\)
গণনা:
ধাপ 1: সবচেয়ে ভেতরের ভগ্নাংশটি সরলীকরণ করুন
⇒ \(2+\frac{1}{3} = \frac{6+1}{3} = \frac{7}{3}\)
ধাপ 2: পরবর্তী ভগ্নাংশে প্রতিস্থাপন করুন
⇒ \(5+\frac{1}{\frac{7}{3}} = 5+\frac{3}{7} = \frac{35+3}{7} = \frac{38}{7}\)
ধাপ 3: পরবর্তী ভগ্নাংশে প্রতিস্থাপন করুন
⇒ \(1+\frac{1}{\frac{38}{7}} = 1+\frac{7}{38} = \frac{38+7}{38} = \frac{45}{38}\)
ধাপ 4: চূড়ান্ত অভিব্যক্তিতে প্রতিস্থাপন করুন
⇒ \(1+\frac{1}{\frac{45}{38}} = 1+\frac{38}{45} = \frac{45+38}{45} = \frac{83}{45}\)
∴ মানটি \(\frac{83}{45}\) = \(1 \frac{38}{45}\)
Last updated on Jun 17, 2025
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