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

What is the simplified value of $(2+1)(2^{2}+1)(2^{4}+1)(2^{8}+1)?$

When $\frac{1}{4}$ of a number is subtracted from $\frac{1}{3}$ of the same number,the remainder obtained is $12$. The number is:

What will come in the place of the question mark $(?)$ in the following expression?
$\sqrt{15^{2} \times 12 \div 9 - 125 + 21} = ?$

Along a yard $225 \ m$ long,$26$ trees are planted at equal distances,with one tree at each end of the yard. What is the distance between two consecutive trees in meters?

If $a+b+c=1$ and $ab+bc+ca=\frac{1}{3}$,then $a:b:c$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module