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dey
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Find the series sum ln2/2 – ln3/3 + ln4/4 – ln5/5 + ….
The formula for finding the sum of an infinite series is S = a / (1-r), where 'a' is the first term of the series and 'r' is the common ratio.
Yes, the sum of an infinite series can be negative if the series has alternating positive and negative terms. In this case, the sum will alternate between positive and negative values.
An infinite series will converge if the absolute value of the common ratio (|r|) is less than 1. If |r| is greater than or equal to 1, the series will diverge.
Yes, there are special cases such as when the common ratio (r) is equal to 1. In this case, the series will either diverge or have no defined sum. Another special case is when the first term (a) is equal to 0, in which case the sum of the series will be 0.
If the series does not follow a specific pattern or the common ratio (r) is not constant, the formula for finding the sum of an infinite series may not apply. In these cases, other methods such as the Ratio Test or the Root Test may be used to determine the convergence or divergence of the series.