Telescoping series is a series where all terms cancel out except for the first and last one. This makes such series easy to analyze.
Why is it called a telescoping series?
It’s now time to look at the second of the three series in this section. In this portion we are going to look at a series that is called a telescoping series. The name in this case comes from what happens with the partial sums and is best shown in an example. We first need the partial sums for this series.
What does telescoping mean in math?
In mathematics, a telescoping series is a series whose general term can be written as , i.e. the difference of two consecutive terms of a sequence .
How do you know if convergence is telescoping?
Defining the convergence of a telescoping series
s n = ∑ i = 1 n a i = a 1 + a 2 + . . s 4 = ∑ i = 1 4 a i = a 1 + a 2 + a 3 + a 4 s_4=sum_{i=1}^4 a_i=a_1+a_2+a_3+a_4 s4=∑i=14ai=a1+a2+a3+a4s 4 = a 1 + a 2 + a 3 + a 4 s_4=a_1+a_2+a_3+a_4 s4=a1+a2+a3+a4s = lim n → ∞ s n = ∑ n = 1 ∞ a n = a 1 + a 2 + a 3 + .
Is a telescoping series convergent or divergent?
Telescoping series is a series where all terms cancel out except for the first and last one. This makes such series easy to analyze.
What does the geometric series converge to?
The convergence of the geometric series depends on the value of the common ratio r: If |r|
What does telescoping mean in literature?
The contraction of a phrase, word, or part of a word, on the analogy of a telescope being closed: biodegradable for biologically degradable; sitcom for situation comedy.
