Use Theorems 11.2.7-11.2.9 and properties 11.4.11, 11.4.12, and 11.4.13 to derive each statement in 27-30.
Derive the statement:
For all real numbers b and r with b > 1 and r > 0, for all sufficiently large real numbers x. thus there exists a real number k such that for all real numbers n > k ( b = 2 and r = 1):
Note that it is safe to assume that . Multiplying both sides of the inequality by 5n, we obtain
Adding n2 to each side of the inequality, we obtain
However, is positive when n >1 (as n2 > 0, n > 0 and ) and 6n2 is nonnegative
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