Attached files has 5 True or False questions. Thx ac

We wish to determine whether each of the following statements is true or false.
1. If the sequence  ka converges, then it has only one limit, i.e., if 1ka L and 2 ,ka L
then 1 2.L L
This is true. First suppose 1ka L . Then for all 0,  there exists a positive number 1N
such that 1ka L   for all 1.k N Next suppose 2ka L . Then for all 0,  there
exists a positive number 2N such that 2ka L   for all 2.k N Now suppose 1ka L
and 2ka L . Let  1 2max , .N N N Then for all ,k N we have 1ka L   and
2ka L   . Thus by the triangle inequality, we have
1 2 1 2
2 .
k kL L L a a...