Convergence And Divergence Of Series

Question 1

How can you tell the convergence for a geometric series (rⁿ)?

Answer 1

If r < 1, the series converges.
r > 1 the series diverges.

Question 2

What can you say for series written in the form of 1/n^p?

Answer 2

If P > 1, the series converges.
If P ≤ 1, the series diverges.

Question 3

What is the formula for the ratio test?

Answer 3

Limit (n→∞) [ U_n+1 / U_n ] = L
If L > 1, the series diverges.
If L < 1, the series converges.
If L = 1, the series fails
The contents of the square bracket are made positive if their solution gives a negative answer by the way.