Klik op de formule en het bewijs komt rechts

	01
	02
1.2 + 2.3 + 3.4 + ... + n.(n + 1)  =  n (n + 1)(n + 2)	65
1.3 + 2.4 + 3.5 + ... + n(n+2) =  n(n+1)(2n+7)	C4
1.4 + 2.7 + 3.10 + ... + n.(3n + 1) = n.(n + 1)²	H7
1.5 + 2.6 + 3.7 +...+ n(n+4) =  n(n+1)(2n+13)	I6
1 + 2 + 4 + 8 + 16 + ... + 2n−1 = 2n − 1	17
1 + 4 + 7 + ... + (3n − 2) =  n (3n − 1)	M8
2 + 8 + 14 + ... + (6n − 4) = 3n² − n	N3
2+7+14+23+...+(n2+ 2n−1) =  n(2n2+ 9n+1)	O3
20 + 21 + 22 + ... + 2n = 2n + 1 − 1	L2
1² + 2² + 3² + ... + n² =  n (2n + 1)(n + 1)	36
1³ + 3³ + 5³ + ... + (2n − 1)³ = 2 n⁴ − n²	38
1³ + 2³ + 3³ + ... + (2n)³ = n².(2n + 1)²	K4
1.1! + 2.2! + 3.3! + ... + n.n! = (n+1)! − 1	03
1.2.3 + 2.3.4 + ... + n(n+1)(n+2) =  n(n+1)(n+2)(n+3)	39
	40
1.2² + 2.3² + ... + (n−1).n² = n(n²−1)(3n+2)	O2
2³ + 4³ + 6³ + ...(2n)³ = 2 n²(n + 1)²	41
(1² +1).1! + (2² +1).2! + ... + (n² +1).n! = n.(n + 1)!	42
1² − 3² + 5² −7² + ... + (4n − 3)² − (4n − 1)² = −8n²	43
1.3 + 3.5 + 5.7 +... + (2n−1)(2n+1) =  n.(4n² + 6n − 1)	47
2.2 + 3.22 + 4.23 + 5.24 + ... + (n+1).2n = n.2n+1	S1
1.3 + 2.32 + 3.33 + 4.34 + ... + n.3n =  [ (2n − 1).3n + 1]	59
1² + 2² + 3² + ... + n² =  n(2n+1)(n+1)	36
1³ + 2³ + 3³ + ... + n³ =  n².(n + 1)²	37
14+ 24+ 34+...+ n4 =  n(n+1)(2n+1)(3n2+3n−1)	I3
15+ 25+ 35+...+ n5 =  n2(n+1)2(2n2+2n−1)	I5
1³ + 2³ + 3³ + 4³ +...+ n³ = (1 + 2 + 3 + 4 +...+ n)²	06
(21−1) + (22−1) + ... + (2n −1) = 2n+1 −n−2	10
F1 + F2 + F3 + ... + Fn = Fn+2 − 1 (FIBONACCI)	C5
	J5
F5n  is een vijfvoud   (FIBONACCI)	O5
	B5
F1 + F3 + F5 + ... + F2n−1  =  F2n  (FIBONACCI)	67
Fn−1 . Fn+1 = Fn2 + (− 1)n  (FIBONACCI)	91
2.2 + 3.22 + 4.23 + ... + (n+1).2n = n.2n+1	H8
1.21 + 2.22 + 3.22 + ... + n.2n = (n − 1).2n+1 + 2	70
12 − 22 + 32 − ... + (− 1)n−1.n2  =  (−1)n−1.n.(n+1)	72
12+ 32+ 52+ ... + (2n − 1)2 = n.(4n2 − 1)	64
1 + 2 + 3 + ... + n  =  Cn2 + n   ( n = 2, 3, ...)	96
	A0
1 + (1+3.1) + (1+3.2) + ... + (1 + 3n) = (n+1)(3n+2)	A6
	A8
	E0
	E6
	N6
1.n + 2(n−1)+3(n−2)+...+(n−1).2 + n.1 =  n(n+1)(n+2)	F0
1².2! + 2².3! + ... + n²(n + 1)² = (n + 2)!.(n − 1) + 2	F2
2 + 2.3 + 2.32 + 2.33 + ... + 2.3n−1 = 3n − 1	J0
(21 + 1)(22 + 1)(24 + 1)(28 + 1)...(2(2n−1) + 1) = 2(2n) − 1	K2
som van derde machten van drie ...	R4

  V o l l e d i g e   i n d u c t i e
Mathematical induction   (Engels)
Vollständige Induktion   (Duits)
Induction Mathématique (Frans)
Indução matemática (Portugees)
Induzione matematica (Italiaans)
Inducción completa   (Spaans)

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