Sequences & Series Flashcards
Arithmetic sequence formula
Un = a + (n-1)d
Arithmetic series formulas
Sn = n/2 (2a + (n-1)d) OR Sn = n/2(a+L)
How to work out arithmetic series formula
Write out terms a + (a+d) + (a+2d) + … + (a+(n-1)d)
Write out terms reversed
(a+(n-1)d) + … + (a+2d) + (a+d) + a
Add them: 2Sn = n(2a + (n-1)d)
Divide by 2: Sn = n/2(2a+(n-1)d)
Geometric sequence formula
Un = ar^n-1
Geometric series formula
Sn = a(1-r^n) / 1-r OR Sn = a(r^n -1) / r-1
How to work out geometric series formula
Sn = a + ar + ar^2 … ar^n-2 + ar^n-1
make another and times by r, then minus rSn from Sn
Sn - rSn = a - ar^n
Take out common factor:
Sn (1-r) = a(1-r^n)
divide by 1-r: Sn = a(1-r^n) / 1-r
What is sum to infinity
S = a / 1-r
What does divergent series mean
terms of series are getting larger
What does convergent series mean
terms of series are getting smaller
How to know if series is convergent
if |r| < 1