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Evaluate the limit:
Let and . Prove that the equation
has no solution.
Without loss of generality , assume that . If held , then it would be thus . It follows from Bernoulli’s inequality that,
which is an obscurity. The result follows.
Let be a continuous function and be the set of all positive integers such that there exists such that
Prove that is infinite and evaluate the limit
Let denote the factorial of a real number; that is . Evaluate the limit:
It holds that
where denotes the -th harmonic number and the Euler – Mascheroni constant.