3.4.08 Limit Intro3
Download as PPT, PDF2 likes733 views
The document discusses the harmonic sequence, which is the sequence of reciprocals of positive integers. The limit of the harmonic sequence as n approaches infinity is zero, meaning the values get infinitely close to zero as n increases. The document provides examples of sequences that converge, having a limit, and diverge, not having a limit, as n approaches infinity.
1 of 8
Downloaded 26 times
More Related Content
What's hot (15)
Ad
Viewers also liked (20)
Ad
Similar to 3.4.08 Limit Intro3 (20)
More from chrismac47 (20)
Recently uploaded (20)
3.4.08 Limit Intro3
- 1. The Harmonic Sequence The Harmonic Sequence is the sequence of reciprocals of the positive integers.
- 2. The Harmonic Sequence The limit of the Harmonic Sequence, as n approaches infinity, is zero. This means that as n increases, the values in the sequence get closer and closer to zero. 0.000000000001 1,000,000,000,000 0.000001 1,000,000 0.001 1000 0.01 100 H n n
- 3. You can use a calculator to investigate limits… To examine the Harmonic Sequence, set Then press 2 nd -> TBLSET to decide what values of x (which has replaced n ) to look at. We want to look at large numbers.
- 4. Not all sequences have limits as n->∞. Those that do are said to converge . If they do not, they are said to diverge . The sequence a n = n diverges, because the values increase without bound. Examine the following sequences. State whether the sequence converges or diverges. If it converges, find the limit: Diverges – the limit does not exist…
- 6. How can we put this to use?
- 7. Now, try it with these:
- 8. What’s that you say? More?