Page 13 - Math SL HB Sem 1

SEQ{JENCES

Definition:
A sequence is a set olquantilies
ur,ur,u_,.-.,u,
,... arranged in a dellnite
order rvhere n eZ,
(a) Finite sequence i ut,u2,ur,.-.,un
(b) Infinite sequence: l/r , u2 , r/i ,..., zr,,

Examples
(i) I,4,9,16,...,64
I ll
(iD I
3' 9'27'"'
(iii) l, I ,2,3,5,8,13...
(Fibonacci sequence)

Note: Any scquence whose tenns approach one finite value is said to be convergent
I 7 3 4
Consider the sequence
-,-,-,-,.. All the terms are less than I, and as the
sequence progresses, the value ofthe terms is getting closer to l. We say that the
sequence conr.ergcs.

rhar is nor convergent
l^._1-ri:*.: is called divergcnr.
Lonstder the sequence 2,4.6.9,10,...
The terms are increasing without limit, so this sequence is clearly divergent

s Ft,rtt lis

Definition:
The sum of the terms of a sequence is called a series.
:
(a) Finite series: S,
ut +uz + uj + ...+ un
(b) Infinite series: S_ = ut+u2+u3+...+un+...

2-t