Calculus Volume 2 · free preview
Sequences
A sequence is a list of numbers indexed by the integers, converging when its terms settle toward a single limit, with the limit laws, monotonicity, and boundedness deciding convergence.
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.
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