epdf.pub_the-nuts-and-bolts-of-proofs-third-edition-an-intr

106 The Nuts and Bolts of Proofs
33. Let k > 6 be an integer. Then 2^ > (k + 1)1
34. There exists a number k such that 2^>(/c + 1)^.
35. If r is a rational number and ^ is a rational number, then t + g is an
irrational number.
36. There are three consecutive integer numbers a, fc, and c such that 3
divides a -\- h -\- c. (See Exercise 28.)
37. Let n be an integer. If n is a multiple of 5, then n^ is a multiple of 125.
38. For every integer n the number n^ + n is always even.
39. Let k>6 be an integer. Then k\>k^.
40. Let I dn = ^^4^ I . Then lim a„ does not exist.