LCKurtz

You have the right idea, but it isn't written well. You need to use your observations to write your argument in reverse. Something like this:

Given ca_n [itex]\rightarrow[/itex] L we will show that a_n [itex]\rightarrow[/itex] L/|c|, which is a contradiction.

Suppose[itex]\ \epsilon > 0[/itex]. Then there is N > 0 such that:

| ca_n - L| < |c|[itex]\epsilon [/itex]

for all n > N. Therefore

|ca_n - L| = |c(a_n - L/c| = |c||(a_n - L/c| < |c|[itex]\epsilon[/itex]

which gives, upon dividing that last inequality by |c|, | a_n - L/c| < [itex]\epsilon[/itex]
for all n > N.