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I have a Calculus II question? Help please?
What does it mean converges and diverges? (Sequences)
For example:
{n/(n+1)}[n=0, +inf]
limn->in~n/n=1 I think it means that the sequence goes to 1 ( the last term of the sequence is 1?) { 1/2, 2/3, 3/4, 4/5, ......1} am I right? what does 1 means?
1 Answer
- ?Lv 77 years agoFavorite Answer
A convergent sequence approaches a finite value, more and more closely, as n gets larger.
A divergent sequence grows larger without limit as n gets larger.
Here, we have:
...........n
lim ....------
n→∞..n+1
As n gets very large, the difference between n and n+1 gets very small:
1 ÷ 2 =0.5
1000 ÷ 1001 = 0.999+
1,000,000 ÷ 1,000,001 | 0.999999+
1,000,000,000 ÷ 1,000,000,001 = 0.999999999+
In the limit, the quotient goes to 1; or, the series converges to 1.