Root test

The root test is a way to check if a series is convergent or divergent. We use the root test when we have a series that consists of non-negative terms, which means that all the terms are bigger than or equal to zero.

To use the root test, we take the nth root of the absolute value of each term in the series. If the limit of the nth root of the absolute value of the nth term of the series is less than 1, then the series converges (it means that the series has a sum that it approaches towards). If the limit is greater than 1, then the series diverges (in other words, it means that the series does not have a sum that it approaches towards).

It is like measuring how much the series is growing at each step by taking the nth root of the absolute value of the nth term. If the growth is less than 1, the series does not grow too much, and it is convergent. If the growth is more than 1, the series is growing too much, and it is divergent.

It's important to note that the root test only works for series with non-negative terms. If the series has terms that go below zero or are negative, we need to use other tests to see if they are convergent or divergent.