The value of frac{1}{2+frac{1}{2+frac{1}{2-fr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) To solve the expression $\frac{1}{2+\frac{1}{2+\frac{1}{2-\frac{1}{2}}}}$,we simplify from the bottom up.First,simplify the innermost fraction: $2

Vedclass · Accepted Answer

$\frac{8}{19}$

Vedclass · Answer

(D) To solve the expression $\frac{1}{2+\frac{1}{2+\frac{1}{2-\frac{1}{2}}}}$,we simplify from the bottom up.First,simplify the innermost fraction: $2 - \frac{1}{2} = \frac{4-1}{2} = \frac{3}{2}$.Now,substitute this back into the expression: $\frac{1}{2+\frac{1}{2+\frac{1}{3/2}}} = \frac{1}{2+\frac{1}{2+\frac{2}{3}}}$.Next,simplify the denominator $2 + \frac{2}{3} = \frac{6+2}{3} = \frac{8}{3}$.Substitute this back: $\frac{1}{2+\frac{1}{8/3}} = \frac{1}{2+\frac{3}{8}}$.Finally,simplify the denominator $2 + \frac{3}{8} = \frac{16+3}{8} = \frac{19}{8}$.Thus,the expression becomes $\frac{1}{19/8} = \frac{8}{19}$.

The value of $\frac{1}{2+\frac{1}{2+\frac{1}{2-\frac{1}{2}}}}$ is

Similar Questions

If $2 = x + \frac{1}{1 + \frac{1}{3 + \frac{1}{4}}}$,then the value of $x$ is

What will come in the place of the question mark $(?)$ in the following expression?
$\frac{28}{65} \times \frac{195}{308} \div \frac{39}{44} + \frac{5}{26} = ?$

If $\frac{1}{\sqrt{a}} - \frac{1}{\sqrt{b}} = 0$,then the value of $\frac{1}{a} + \frac{1}{b}$ is

If $x^{2} + \frac{1}{x^{2}} = 1$,then what is the value of $x^{48} + x^{42} + x^{38} + x^{30} + x^{24} + x^{18} + x^{12} + x^{6} + 1$?

What is the value of the positive square root of $(69 + 28 \sqrt{5})$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module