Summary AP Calculus BC – Series (Full Notes + Solved Problems + Answer Keys)

SEQUENCES AND SERIES

SEQUENCES
s called a sequence
9
ÇEÇE
tüm
wr tethe f rst 5 terms of the sequence an III
A az az 9 as

constant
Asequence converges f l man
otherw se t d verges


Does the sequence an 3J converge

hm converges


Does the sequence an converge

h ç 7h o d verges

Does the sequence an converge

hç 0 converges

, SERIES


An A da A
1 1

A ser es s essent ally thesum of a sequence

A ser es converges f the sun approaches
a constant Th s s not as easy as t s for
sequences to determ ne

There are several tests to check convergence


1 L m t Test

For an

f h çAn 0 the ser es DIVERGES


That doesn't guarantee convergence f f gan D

Apply other tests n th s scenar o

, Does the ser es
4 converge or d verge


hç 2 the ser es d verges



Does the ser es 85 converge or d verge

8h72
tho 0 the test s Moonclus ve
3en apply other tests



2 Geometr c Ser es Test

ar a Ar d rt ar

Th s s called a geometr c ser es w th common rat o r

A geometr c ser es converges f r 1
It s poss ble to
calculate the sum of a convers ng
geometr c ser es us ng
the formula 5

, Does the ser es 3 7 converge or d verge


3
7 3 3 3

A geometr c ser es w th r

It converges s nce r C1

EX
Does the ser es 4 converge or d verge

A geometr c ser es w th r

It d verges s nce 1171


F nd the sum of the ser es
A geometr c ser es w th r t converges


5
1