Question

If `a_n` converges and `lim_(n->oo) a_n /b_n=0`, where c is a constant, does `b_n` necessarily converge?

Answer 1

No

Explanation:

Example

• `a_n = 1/n`
• `b_n = n`

`lim_{n -> oo} a_n = 0`

`lim_{n -> oo} b_n = oo`

`lim_{n -> oo} a_n/b_n = 0`