What is a convergent infinite series?

Answer 1

An infinite series #sum_{i=1}^infty a_i# is said to be convergent if #lim_{n to infty}S_n# exists, where #S_n=a_1+a_2+a_3+cdots+a_n#.

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Answer 2

Christopher Agresta

A convergent infinite series is a series of numbers where the sum of its terms approaches a finite value as more terms are added. In other words, as you take the sum of more and more terms in the series, the total sum eventually stabilizes or approaches a specific finite value. If the sum approaches a finite value, the series is said to converge. Conversely, if the sum does not approach a finite value, the series is said to diverge. Convergence is a fundamental concept in the study of infinite series in mathematics, particularly in calculus and real analysis.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.