1.

Find the value(approx.) of \(3 + \frac{4}{{5 + \frac{7}{{2 + \frac{6}{{8 + \frac{7}{{2 + \frac{1}{3}}}}}}}}}\)1. 52. 43. 74. 8

Answer» Correct Answer - Option 2 : 4

Calculation: 

Calculate this continued fraction from bottom

\( ⇒ 3 + \frac{4}{{5 + \frac{7}{{2 + \frac{6}{{8 + \frac{7}{{2 + \frac{1}{3}}}}}}}}}\)

\( ⇒ 3 + \frac{4}{{5 + \frac{7}{{2 + \frac{6}{{8 + \frac{{21}}{7}}}}}}}\)

\( ⇒ 3 + \frac{4}{{5 + \frac{7}{{2 + \frac{{6}}{{11}}}}}}\)

\( ⇒ 3 + \frac{4}{{5 + \frac{{77}}{{28}}}}\)

\( ⇒ 3 + \frac{{112}}{{217}}\)

\( ⇒ \frac{{763}}{{217}}\)

⇒ 109/31

∴ The value(approx.) of 4.

Note:

109/31 = 3.51, According to the question and given Option 4 is the correct answer, 4 is the nearest approx value.



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