Science:Math Exam Resources/Courses/MATH101 B/April 2024/Question 20 (b)/Hint 1

Consider the behavior of $f(n)$ as $n\to \infty$. What must be true about $c-f(n)$ for the series $S$ to converge? Think about how the terms behave and recall the basic divergence test, which states that a series $\sum a_{n}$ can only converge if $a_{n}\to 0$.