Find the sum of the infinite series

Thread starter dey
Start date May 25, 2013
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Infinite Infinite series Series Sum

In summary, the formula for finding the sum of an infinite series is S = a / (1-r). The sum of an infinite series can be negative if it has alternating positive and negative terms. To determine if an infinite series converges or diverges, check if the absolute value of the common ratio (|r|) is less than 1. There are special cases where the formula may not apply, such as when r=1 or a=0. If the series does not follow a specific pattern or the common ratio is not constant, other methods like the Ratio Test or Root Test may be used.

May 25, 2013

dey

Find the series sum ln2/2 – ln3/3 + ln4/4 – ln5/5 + ….

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May 25, 2013

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Is this homework? If yes, please post it in the homework section and follow the template there.
Even if not, what do you think? Did you calculate some values?

Related to Find the sum of the infinite series

1. What is the formula for finding the sum of an infinite series?

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.

2. Can the sum of an infinite series be negative?

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.

3. How can I determine if an infinite series converges or diverges?

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.

4. Are there any special cases in which the formula for finding the sum of an infinite series does not apply?

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.

5. How do I know if I need to use a different method to find the sum of an infinite series?

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.