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g01
groen02
1.2 + 2.3 + 3.4 + ... + n.(n + 1)  = 1/3 n (n + 1)(n + 2) groen 65
1.3 + 2.4 + 3.5 + ... + n(n+2) = 1/6 n(n+1)(2n+7) groen C4
1.4 + 2.7 + 3.10 + ... + n.(3n + 1) = n.(n + 1)² groen H7
1.5 + 2.6 + 3.7 +...+ n(n+4) = 1/6 n(n+1)(2n+13) groen I6
1 + 2 + 4 + 8 + 16 + ... + 2n−1 = 2n − 1 groen 17
1 + 4 + 7 + ... + (3n − 2) = 1/2 n (3n − 1) oranje M8
2 + 8 + 14 + ... + (6n − 4) = 3n² − n oranje N3
2+7+14+23+...+(n2+ 2n−1) = 1/6 n(2n2+ 9n+1) oranje O3
20 + 21 + 22 + ... + 2n = 2n + 1 − 1 groen L2
1² + 2² + 3² + ... + n² = 1/6 n (2n + 1)(n + 1) oranje 36
1³ + 3³ + 5³ + ... + (2n − 1)³ = 2 n⁴ − n² oranje  38
1³ + 2³ + 3³ + ... + (2n)³ = n².(2n + 1)² rood  K4
1.1! + 2.2! + 3.3! + ... + n.n! = (n+1)! − 1 oranje 03
1.2.3 + 2.3.4 + ... + n(n+1)(n+2) = 1/4 n(n+1)(n+2)(n+3) oranje  39
oranje  40
1.2² + 2.3² + ... + (n−1).n² = 1op12n(n²−1)(3n+2) oranje  O2
2³ + 4³ + 6³ + ...(2n)³ = 2 n²(n + 1)² groen  41
(1² +1).1! + (2² +1).2! + ... + (n² +1).n! = n.(n + 1)! oranje  42
1² − 3² + 5² −7² + ... + (4n − 3)² − (4n − 1)² = −8n² r  43
1.3 + 3.5 + 5.7 +... + (2n−1)(2n+1) = 1/3 n.(4n² + 6n − 1) r 47
2.2 + 3.22 + 4.23 + 5.24 + ... + (n+1).2n = n.2n+1 o S1
1.3 + 2.32 + 3.33 + 4.34 + ... + n.3n = 3/4 [ (2n − 1).3n + 1] r 59
1² + 2² + 3² + ... + n² = 1/6 n(2n+1)(n+1) g 36
1³ + 2³ + 3³ + ... + n³ = 1/6 n².(n + 1)² g 37
14+ 24+ 34+...+ n4 = 1op30 n(n+1)(2n+1)(3n2+3n−1) roodI3
15+ 25+ 35+...+ n5 = 1/12 n2(n+1)2(2n2+2n−1) roodI5
1³ + 2³ + 3³ + 4³ +...+ n³ = (1 + 2 + 3 + 4 +...+ n)² oranje 06
(21−1) + (22−1) + ... + (2n −1) = 2n+1 −n−2 groen10
F1 + F2 + F3 + ... + Fn = Fn+2 − 1 (FIBONACCI) groenC5
groenJ5
F5n  is een vijfvoud   (FIBONACCI) groen O5
oranje B5
F1 + F3 + F5 + ... + F2n−1  =  F2n  (FIBON.) oranje 67
Fn−1 . Fn+1 = Fn2 + (− 1)n  (FIBONACCI) rood91
2.2 + 3.22 + 4.23 + ... + (n+1).2n = n.2n+1 oranjeH8
1.21 + 2.22 + 3.22 + ... + n.2n = (n − 1).2n+1 + 2 oranje70
12 − 22 + 32 − ... + (− 1)n−1.n2  =  1/2 (−1)n−1.n.(n+1) rood72
12+ 32+ 52+ ... + (2n − 1)2 = 1/3 n.(4n2 − 1) oranje64
1 + 2 + 3 + ... + n  =  Cn2 + n   ( n = 2, 3, ...) oranje96
oranjeA0
1 + (1+3.1) + (1+3.2) + ... + (1 + 3n) = 1/2 (n+1)(3n+2) oranjeA6
groenA8
roodroodE0
oranjeE6
oranjeN6
1.n + 2(n−1)+3(n−2)+...+(n−1).2 + n.1 = 1/6 n(n+1)(n+2) roodF0
1².2! + 2².3! + ... + n²(n + 1)² = (n + 2)!.(n − 1) + 2 oranjeF2
2 + 2.3 + 2.32 + 2.33 + ... + 2.3n−1 = 3n − 1 groenJ0
(21 + 1)(22 + 1)(24 + 1)(28 + 1)...(2(2n−1) + 1) = 2(2n) − 1 oranjeK2
som van derde machten van drie ... oranjeR4


  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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