n Toekomstige waarde a - AdMaths

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Formele bewys van som-formule vir 'n meetkundige ry.
(Deel van Gr 12 Wiskunde Vraestel 1.)
Beskou die meetkundige ry:
2 n 1
a ar ar ... ar
waar T a eerste term,
1
r konstante verhouding
n
n
n 1
en T ar algemene term
n
n
n n
n
n
n
n
2 n 1
2 n 1
Stel S a ar ar ... ar ..........
2 n 1 n
( r) r S ar ar ... ar ar .......
: r S S ar a
S (r 1) a(r 1)
S
a ar ar ... ar
OPSOMMING:
n
a(r 1)
r 1
n
a(r 1)
r 1
n
11 MOD 3
as r 1
a(1 r )
of as r 1
1 r
2 n 1
S 1 x x ............ x
xn1 x 1
n 1
2 3 n 1 n x 1
EN Sn 1 1 x x x ... x x as x 1
x 1