Calculus Volume 2 · 免费预览
发散判别法与积分判别法
发散判别法重述了第 n 项条件，而积分判别法将正项级数与反常积分进行比较，二者同敛同散，其中 p-级数的分类是它最精确的应用。
1. The divergence test
The divergence test
2. The integral test
The integral test
3. The p-series
The p-series
4. Remainder estimates
Remainder estimates
5. Divergence test direction
The divergence test certifies divergence when which condition holds?
6. Integral test hypotheses
The integral test applies to a series whose terms come from f(n) when f satisfies which conditions?
7. P-series threshold
The p-series sum of 1/n^p converges for which exponents?
8. Remainder upper bound
After N terms of a convergent p-series with p = 2, the remainder R_N is at most which integral?
9. Terms not needed condition
The series sum of (n + 1)/n diverges by which observation?
10. Integral of one over x squared
The improper integral from 1 to infinity of dx/x^2 equals what number? Answer with a number.
11. Harmonic integral divergence
The integral from 1 to infinity of dx/x equals what function of the upper limit? Answer with a function like ln b.
12. Remainder of sum one over n cubed
After N terms of sum 1/n^3, the remainder is at most 1 over (2 N^2). As a power, what is the exponent of N? Answer with a number.
13. Zeta at two
The sum of 1/n^2 equals pi^2/6, a famous value. Which test certifies its convergence without giving the sum?
14. Test sharing
The integral test's conclusion is that the series and integral share which fate? Answer with one word, convergence or divergence.