samenvatting/formule blad Wisunde A Domein D verandering
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Course
Wiskunde A
Level
VWO / Gymnasium
Dit is het formule/samenvattings blad dat ik gemaakt heb ter voorbereiding van mijn centraal eindexamen Wiskunde A VWO.
Op dit blad staat alle informatie kort aangestipt wat je moet kennen voor het domein D verandering.
Ook heb ik een blad voor domein B en een blad voor domein C. Met al deze ...
3.1 RECURSIEVE FORMULE 3.2 DIRECTE FORMULE
o rekenkundige rij o Rekenkundige rij
- a(n) = a(n-1) + v met a(0) - a(n) = a(0) + vn
- a(n) = a(1) + v(n-1)
o meetkundige rij
- a(n) = r × a(n-1) met a(0) o Meetkundige rij
- a(n) = a(0) × rn
3.3 DE SIGMANOTATIE - a(n) = a(1) × rn-1
o ∑𝑛𝑘=0 𝑢𝑘 = u0 + u1 + u2 + u3 .. + un
o Van directe naar recursieve formule
1 1
a(n) = 2 𝑛2 + 𝑛
- ∑3𝑘=0 𝑢𝑘 met uk = 2n2 +3n 1
2
1
a(n-1) = 2 (𝑛 − 1)2 + (𝑛 − 1)
Gr: u(n) = 2n2 +3n 1 1
2
Tabel = 0 + 5 + 14 + 27 = 46 = 𝑛2 − 𝑛
2 2
1 1 1 1
a(n) – a(n-1) = 2 𝑛2 + 2 𝑛 − (2 𝑛2 − 𝑛)
2
3.4 RECURSIEVE FORMULE SOMRIJ =n
o S(n) = S(n-1) + u(n) met S0 = u0 a(n) = a(n-1) + n met a(1) = 1
o S(n) = ∑𝑛𝑘=0 𝑢𝑘
3.5 RIJEN OPPERVLAKTE EN OMTREK
Gegeven is rij u(n) = 2u(n-1) -3n met 1. reken oppervlakte of omtrek van
u(0)= 10 en de bijbehorende somrij S(n) de eerste figuren uit.
Geef de recursieve formule van S(n)
O(1) = a O(2) = b O(3) = c
- S(n) = S(n-1) + 2u(n-1) -3n
2. bereken r
𝑏 𝑐
Bereken S(10) 𝑒𝑛 = r
GR: Nmin = 0 𝑎 𝑏
U(n) = 2u(n-1) -3n
U(0) = 10 3. stel formule op
V(n) = v(n-1) + 2u(n-1) -3n - directe
V(0) = 10 - recursieve
Tabel geeft: S(10) = 8419
3.6 SOORTEN VAN STIJGEN EN DALEN
1
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