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SERIES TEST - Coggle Diagram
SERIES TEST
CAUCHY CONDENSATION TEST
double implication
useful in log
AN NON INCREASING SEQUNCE
A2N *2N IF ONLY IF
DIRCHLET TEST
sequence decreasing
abels test
a series partial sums are bounded
RATIO TEST
LIMSUP OF AN+1/AN MOD
LESS THAN 1 ABSOLUELTY CONVEREGNT
LIMINF AN+1/AN
GRETAER THAN 1 THEN DIVERG
L C TESET
double implies in one case
positive is important
ALEGBRA OF SERIES
SUM OR DIFFERENCE
PRODUCT NOT ALWAYS
IMPORTANT NOTE FOR THE RADIUS OF CONVERGENCE
THE SERIES MUST BE ABSOLUELTY CONVERGENT
SO USE ONLY ROOT TEST RATIO TEST
BUT WHEN TALK OF INTERVAL OF CONVERGENCE THEN YOU CAN USE ANY OF THESE TESTS
ROOT TEST
lim sup of anmod 1/n
less than 1 absoluelty convergent
greater than 1 diverges
equal inconsistent
COMPARISON TEST
postive is important only single implication
NTH TERM TEST
IF NTH TERM DOESNT GO TO ZERO THEN CANNOT BE CONVERGENT
ALTERNATING SERIES TEST
terms have alternting sign and folow the nth term test
1/NP
P>1 convergent
ABSOLUTE CONVERGENCE IMPLY CONVERGENCE