- #1
seroth
- 9
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What exactly is the difference between "increasing/decreasing" and "strictly increasing/decreasing" ? is it similar to conditional and absolute convergence?
An infinite series is a sum of infinitely many terms. It is written in the form of ∑an, where n represents the number of terms and a is the general term of the series.
A decreasing infinite series is a series in which each term is smaller than the previous one. This means that the value of each term is decreasing as n increases.
An increasing infinite series is a series in which each term is larger than the previous one. This means that the value of each term is increasing as n increases.
An infinite series is convergent if the sum of its terms approaches a finite value as n approaches infinity. It is divergent if the sum of its terms does not approach a finite value as n approaches infinity.
A convergent infinite series has a finite sum, meaning that the value of the series approaches a finite number as n increases. A divergent infinite series does not have a finite sum, meaning that the value of the series does not approach a finite number as n increases.