A geometric series is of the following type:
being the0 and r the reason.
Ex: 1 + 2 + 4 + 8 + 16 +…
a = 1
Sum of a geometric series
The geometric series
Converge and have sum if | r | <1.
Diverge if | r | 1.
Be and two series of terms positive. So:
* If , being "ç" a real number then the series are both converging or both divergent.
* If what if converge then also converges.
* If what if diverges then also diverges.
NOTE: If theno is expressed by a fraction, we must consider both the numerator and the denominator of bno only the most important terms.
Ex: Check if the given series converges or diverges:
is a geometric series of 1/3 ratio, so it is convergent. Applying the comparison test, we have:
Therefore, it is concluded that the series converges.Next: P-Series, Alternate Series, and Power Series