Does a series have to start from 1 to be able to apply convergence tests? In the ratio test, for example, we know that the test applies for a sum from n=1 to n=infinity.
Can I directly apply this test to sums from n=x to n=infinity (for example, a sum from n=0 -> infinity)?

Studying the nature of a series means proving if a series converges or diverges. The series sums from n=1 to n=infinity and sums from n=x to n=infinity have the same nature, so the test can be made for any of the series. That is so because finitely terms of the series do not change the nature of the series.
