14. Show that 

15. Show that  for all positive integers n and k.

16. Show the following:

(a) 

(b)  for all positive integers n.

17. Show the following:

(a) 

(b) 
 

18. Show the following:

(a) 1 + 2 + 2² + ... + 2^n-1 = 2ⁿ - 1.

(b)  for all positive integers n.

19. Do the following:

(a) Show that 

(b) Show that  for all positive integers n.

(c) Show by mathematical induction that 

(d) Show that 

20 Show that 
 
 

Monday, June 22, 1998