Basel problem

Reading path

To understand this page from the ground up, read these 64 pages in order. The foundations come first.

1. Harmonic number definition
2. Limit point of a set definition
3. Local maximum definition
4. Sequence definition
5. Limit of a function definition
6. Local minimum definition
7. Real sequence definition
8. Subsequence definition
9. Continuity at a point definition
10. Derivative definition
11. Bounded sequence definition
12. Cauchy sequence definition
13. Geometric sequence definition
14. Limit of a sequence definition
15. Monotone sequence definition
16. Sequence tending to infinity definition
17. Series definition
18. Continuous function definition
19. Fermat's theorem on stationary points statement
20. Limit superior definition
21. Cauchy sequences are bounded statement
22. Sum of a finite geometric series statement
23. Monotone convergence theorem for sequences statement
24. Every sequence has a monotone subsequence statement
25. Convergent sequence definition
26. Pointwise convergence definition
27. Squeeze theorem statement
28. Partial sum definition
29. Power series definition
30. Intermediate value theorem statement
31. Bolzano–Weierstrass theorem statement
32. The sequence r^n tends to zero for |r| < 1 example
33. Radius of convergence definition
34. Uniform convergence definition
35. Convergent series definition
36. Sine and cosine definition
37. Boundedness theorem statement
38. Cauchy criterion for sequences statement
39. Uniform convergence on a set definition
40. Divergent series definition
41. Absolute convergence definition
42. A series of nonnegative terms converges iff its partial sums are bounded statement
43. Series of functions definition
44. Sum of a series definition
45. Extreme value theorem statement
46. Uniformly Cauchy sequence of functions definition
47. Geometric series example
48. Comparison test statement
49. Cauchy condensation test statement
50. Harmonic series example
51. Rolle's theorem statement
52. Root test statement
53. Weierstrass M-test statement
54. Harmonic series diverges statement
55. Mean value theorem statement
56. Cauchy–Hadamard theorem statement
57. p-series test statement
58. Power series converge uniformly on smaller discs inside the radius of convergence statement
59. Uniform convergence of derivatives allows term-by-term differentiation statement
60. Term-by-term differentiation statement
61. Power series are differentiable inside the radius of convergence statement
62. Derivative of cosine statement
63. pi object
64. Basel problem statement