Page 13 - Math SL HB Sem 1

ES

sr.lQrJuNCES

Definition:
A sequcnce is a set olquantities ir,,rrr,ir,,...,i1,,,...
xrrxngcd in adclinite
order where n eZ*

(a) Finite sequence i u1,u2,ut,...,u,
(b) Infinite seq .tence: ut,u2,u.,...,uk,...

Examples:
(, 4 9 6,...,64
I ll
(i') I
3' 9 27',
(iii) l ,l ,2,3,5,8,13,.. (Fibonacci sequence)

Note: Any sequence whose tcnns approach otrc finite value is said to be convergent
| 2 3 4
Consider the sequerce
-,-,-,-,...A11 the terms are less than l. and as the
sequence progresses,
the value olthe terms is getting closer to l. We say that the
sequence converges.

l-.::i*": that is not convergenr is called rlivergent.
L-onsrder the sequencc 2,4,6,9,10,...
'I'he
terms are increasing witlrout limit, so this sequence is clearly divergent

SERItrS

Definition:
I he sum ol- the terms ofa scquencc is callccl a serics.
(a) Finite series: S, - u, + u. + 1\ + ...t.un
(b) Inlinite series: S- - ttt +t\ +u1+._.+Ltnf
...

2-l