Let n > 1 be a positive integer and let a1, a2, ... , a, be real numbers. a) Prove that Σ α <Σ 1ακ . k=1 b) Prove that E ak > la1| - E laxl. E lakl. 'k=1 k=2

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.