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 . Adding 2x to both sides of the inequality, we obtain
However, is positive when n >1 (as n > 0 and ) and 3n is nonnegative when n > 0
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