Consider a version of table expansion where we increase the size of the table by a factor of 10 whenever the table is (For instance, a table with size 10 is expanded to size 100. A table with size 100 is expanded to size 1000 ) Each insertion without table expansion takes (1) tine. Table expansion tales ck time where k is the number of elements in the new table. Initially, the table has size 10. Prove that n insertions into an empty table take a total of (n) tine (an average o (1) time per ins(rtion.) Consider a version of table expansion where we increase the size of the table by a factor of 10 whenever the table is (For instance, a table with size 10 is expanded to size 100. A table with size 100 is expanded to size 1000 ) Each insertion without table expansion takes (1) tine. Table expansion tales ck time where k is the number of elements in the new table. Initially, the table has size 10. Prove that n insertions into an empty table take a total of (n) tine (an average o (1) time per ins(rtion.)