Simplify

1÷[1-2÷{3-4÷($$\overline{2+8}$$​÷5)}]+1:

Correct option is C

Given:​

1 ÷ [1 - 2 ÷ { 3 - 4 ÷ ($$\overline{2+8}$$ ÷ 5)}] + 1

Concept Used:​

​$$\begin{array}{|c|c|} \hline \textbf{Operation preference wise} & \textbf{Symbol} \\\hline\text{Brackets} &[],{}, () \\ \hline \text{Orders, of} & ^x(power), √ (root) , of \\ \hline \text{Division}& ÷ \\\hline \text{Multiplication} & × \\ \hline \text{Addition} & + \\ \hline \text{Subtraction} & - \\\hline\end{array}$$

Solution:

1 ÷ [1 - 2 ÷ {3 - 4 ÷ ($$\overline{2+8}$$​÷ 5)}] + 1

=1÷[ 1 - 2 ÷ {3 - 4 ÷ ($$10$$÷5)}] + 1

=1 ÷ [ 1 -  2 ÷ {3 - 4 ÷ 2}] + 1

=1 ÷ [1 - 2 ÷ 1] + 1

=1 ÷ [1 - 2] + 1

=1 ÷ [-1] + 1

= -1 + 1 = 0