# Math Help - Using combination rules!!! Help please!

1. ## Using combination rules!!! Help please!

True or False, with a proof or counterexample.

a) If bn ≠ 0 and an/bn →1, then an-bn → 0
b) If bn ≠ 0, bn is bounded and an/bn → 1 then an-bn → 0

At the moment I cannot even see which is false so I am struggling with this question. I think the proof will require use of the quotient combination rule and the sum combination rule but I cannot see where to start! Any help would be appreciated!

2. for(a), it is false. Here is a counterexaple: $a_n=n+1, b_n=n,\frac{a_n}{b_n}\to 1$, but $a_n-b_n=1\to 1$.
for(b), It is ture! $\left|a_n-b_n\right|=\left|b_n\right|\cdot\left|\frac{a_n}{b _n}-1\right|\to 0$ since $b_n$ is bounded.