1. Find k > 0 and m ∈ so that 6n3 + 17n ≤ kn3 for all integers n ≥ m. 2. Find k > 0 and m ∈ so that n3 – 7n ≥ kn3 for all integers n ≥ m. 3. For each of the following, prove or give a counterexample...

1. Find k > 0 and m ∈

so that 6n³
+ 17n ≤ kn³
for all integers n ≥ m.

2. Find k > 0 and m ∈

so that n³
– 7n ≥ kn³
for all integers n ≥ m.

3. For each of the following, prove or give a counterexample

(a) If (s_n) converges to s, then (| s_n
|) converges to | s |.

(b) If (| s_n
|) is convergent, then (s_n) is convergent.

(c) lim s_n
= 0 iff lim | s_n
| = 0.