Is there any hard-wired limit on recursion depth in C

Question

The program under discussion attempts to compute sum-of-first-n-natural-numbers using recursion. I know this can be done using a simple formula n

Answer 1

There is no theoretical limit to recursion depth in C. The only limits are those of your implementation, generally limited stack space.
(Note that the C standard doesn't actually require a stack-based implementation. I don't know of any real-world implementations that aren't stack based, but keep that in mind.)

A SIGSEGV can be caused by any number of things, but exceeding your stack limit is a relatively common one. Dereferencing a bad pointer is another.