Calculus Volume 2 · 免费预览
数列
数列是由整数索引的一列数，当其各项趋于某个单一极限时称为收敛，极限定理、单调性和有界性共同决定收敛性。
1. Sequences and limits
Sequences and limits
2. Techniques for limits
Techniques for limits
3. Monotonicity and boundedness
Monotonicity and boundedness
4. Recursively defined sequences
Recursively defined sequences
5. Convergence definition
A sequence a_n converges to L when which condition holds?
6. Dominant term division
To evaluate lim (3n^2 + n)/(2n^2 - 5), which algebraic move applies?
7. Monotone convergence
The monotone convergence theorem states that a sequence which is increasing and bounded above must do what?
8. Oscillation divergence
The sequence a_n = (-1)^n diverges for which reason?
9. Squeeze theorem example
The sequence sin(n)/n converges to what value, by the squeeze theorem?
10. Limit of one over n
The sequence a_n = 1/n converges to what number? Answer with a number.
11. Limit of n over n plus one
The sequence n/(n + 1) converges to what number? Answer with a number.
12. Bounded nonconvergent example term
The bounded divergent example (-1)^n takes which two values? Answer with the smaller number.
13. Growth rate ordering
The sequence n^2/2^n converges to which value, reflecting the growth hierarchy?
14. Monotone theorem name count
The theorem joining monotonicity and boundedness to force convergence is the monotone convergence theorem. As a number, how many hypotheses does it have? Answer with a number.