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TERM 1
nth term test
DEFINITION 1 if the limit as n approaches infinity does not equal 0 then the series diverges. TERM 2
Geometric Series Test
DEFINITION 2 sum of c*r^n from n=0 to infinityif abs( r ) < 1 converges to a0 / ( 1-r )abs( r ) >= 1 diverges TERM 3
Telescoping Series Test
DEFINITION 3 Sum of b sub n - b sub (n+1) converges limit as n approaches infinity of b sub n = L TERM 4
p - Series
DEFINITION 4 Sum of 1/n^p n=1 to infinityconverges p > 1diverges p <= 1 TERM 5
Alternating Series
DEFINITION 5 Sum of (-1)^(n-1)*(a sub n)converges if 0<a sub (n+1) < a sub n & limit as n approaches infinity of a sub n = 0
TERM 6
Integral
DEFINITION 6 an = f(n) >= 0 integrate f(x) from 0 to infinityif integral converges then an converges and vise versa TERM 7
Direct Comparison
DEFINITION 7 compare an to some function bnif 0<=an<=bn and sum bn converges then an convergesif 0<=bn<=an and sum bn diverges then an diverges TERM 8
Limit Comparison
DEFINITION 8 if limit of an/bn as n approaches infinity = L > 0 and sum of bn converges then an convergesif limit of an/bn as n approaches infinity = L > 0 and sum of bn diverges then an diverges TERM 9
Ratio Test
DEFINITION 9 if limit of abs( (a sub (n+1)) / an) as n approaches infinity < 1 then an convergesif limit of abs( (a sub (n+1)) / an) as n approaches infinity > 1 or = infinity then an diverges
