Series Flashcards
Nth term test
Can only show divergence
Limit as n goes to infinity of a sub n does not equal 0, diverges
Geometric series
Absolute value of r<1, converges
Absolute value of r>/equal to 1, diverges
Sum of a geometric series
S= a/(1-r)
P-series
P>1 converges
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Alternating series
0< a sub n+1 < a sub n
Limit as n goes to infinity of a sub n =0
Remainder for alternate series
R = next term
When can use integral test?
When f is continuous, positive and decreasing
Integral test
Integral from 1 to infinity of f(x) converges, converges
Integral from 1 to infinity of f(x) diverges, diverges
Root
Limit as n approaches infinity of the nth root of the absolute value of a sub n <1, converges
“ “ a sub n > 1 diverges
Inconclusive if =1
Ratio
Limit as n goes to infinity of the absolute value of a sub n+1 over a sub n <1, converges
“” >1 diverges
Inconclusive if =1
Direct comparison
If comparison series converges and original series is smaller, converges
If comparison series diverges and original series is bigger, diverges
Limit comparison
Limit as n goes to infinity of original over comparison is +, finite number and comparison converges, converges
“” and comparison diverges, diverges
Absolute convergence
If the absolute value of a sub n converges, series converges
Conditional convergence
If the absolute value of a sub n diverges but a sub n converges
What does the ratio test say about convergence?
If the series converges, it’s absolute
