Is B N convergent or divergent?
In fact, the series diverges since it is comparable to ? 1 n which is divergent since it is a p -series with p ? 1. The title is about the sequence, and the quote box is about the series. You should review your tests: having b n decreasing and converging to 0 does not imply that ? b n is convergent. The classic example is the harmonic series ? 1 n.
Is BN decreasing and converging to 0 convergent?
The title is about the sequence, and the quote box is about the series. You should review your tests: having b n decreasing and converging to 0 does not imply that ? b n is convergent. The classic example is the harmonic series ? 1 n. The series ? 1 2 n is another one. This search and this search in Approach0 return several similar questions.
What is convergent series?
A convergent series exhibit a property where an infinite series approaches a limit as the number of terms increase. This means that given an infinite series, ? n = 1 ? a n = a 1 + a 2 + a 3 + …, the series is said to be convergent when lim n ? ? ? n = 1 ? a n = L, where L is a constant.
Is an infinite series of numbers absolutely convergent?
In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite. More precisely, a real or complex series .