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A-level Mathematics7357

7357

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3.5 D: Sequences and series

 
Content
D1

Understand and use the binomial expansion of

(a+bx)n 
for positive integer
n
; the notations
n!
,
nCr
and
nr
; link to binomial probabilities.

Extend to any rational

n
, including its use for approximation; be aware that the expansion is valid for
bxa<1
. (Proof not required.)

 
Content
D2

Work with sequences including those given by a formula for the

n
th term and those generated by a simple relation of the form
xn+1=fxn
; increasing sequences; decreasing sequences; periodic sequences.

 
Content
D3

Understand and use sigma notation for sums of series.

 
Content
D4

Understand and work with arithmetic sequences and series, including the formulae for

n
th term and the sum to
n
terms.

 
Content
D5

Understand and work with geometric sequences and series including the formulae for the

n
th term and the sum of a finite geometric series; the sum to infinity of a convergent geometric series, including the use of
r<1
; modulus notation.

 
Content
D6

Use sequences and series in modelling.