Linq Select has an override that gives you the index of the current item in the selector (that index is the same number of times you need to repeat). I used Repeat didn't realize there was a string constructor overload that does the same.

Also totally forgot about string.Join. Much cleaner code than I wrote on my first pass.

decided to diversify the same solutions :D

You're returning the last number that's only one digit, read the instructions again:

Write a function, persistence, that takes in a positive parameter num and returns its multiplicative persistence, which is the number of times you must multiply the digits in num until you reach a single digit.

You only have to check if the array is not empty, as easy as that. Fix your code and it'll work.

I love this website because you get to see a lot more of the niche pieces of code, which can be overlooked :)

This is a property which can be pulled through if you want it. I could of named it anything. One the where linq, if you select to name properties (in this case "index"), it will create a property which contains the current interations index. There is another property which can also be pulled through (pretty sure there are 3 properties (1: item of the list, 2: index). Anyway the second name in (n,index) is to reference the index.

Or as Visual Studio 2017 puts it:
Filters a sequence of values based on a predicate. Each element’s index is used in the logic of the predicate function.
Predicate: A function to test each source element for a condition; the second parameter of the function represents the index of the source element.

Anyway... I know both the Select and Where Linq methods allow you to pull through the index.