f nth 𝑛th  root of unity be 1,a1,a2,…an−1,1,𝑎1,𝑎2,…𝑎𝑛-1, then ∑n−1r=112+ar∑𝑟=1𝑛-112+𝑎𝑟 is equal toAn⋅2n−12n−1−1

The question seems to be about complex numbers and their roots of unity. However, the question is not clear due to formatting issues.

The nth roots of unity are the complex numbers which, when raised to the power n, give 1. These roots lie on the unit circle in the complex plane and are evenly distributed around it.

The nth roots of unity can be represented as 1, a1, a2, ..., an-1.

The sum of the nth roots of unity is always 0, except for the 1st root which is 1.

The question seems to ask for the sum of the reciprocals of 1 plus each nth root of unity, which can be written as ∑(1/(1+ar)) for r from 1 to n-1.

However, without further context or clarification, it's not possible to provide a specific numerical answer.

The expression An⋅2n−12n−1−1 seems to suggest some relationship or formula that should be used, but without further information or clarification, it's not clear how this expression relates to the rest of the question.

Please provide more context or clarify the question.