Summary
Convergence Tests Summary
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Condensed summary of all convergence tests covered in class with simple examples.
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3.3.6 convergence testsDivergence Test:
when the nth term does converge
not to zero as n - a
Alternating Series Test:
when successive terms in the series alternate signs
mustbe
decreasing and net 0
=
Integral test:
when
you can substitute X form in then term and
nth get a function you can
integrate
f(x)=0, f(x) < 0
Ratio Test:
n use with powers (7)
simplifies
antic,
any to
when
enough easily compte or
an
factorials (n!)
1
converges, I or +00, diverges
=
-
you may have to do differenttest to find convergence when 1:1
Comparison Test / LimitComparison Test
·
When an Ebn(bn- simpler term) when his very large
·din
if by an
converges so does
·if270 and by diverges. An diverges
if(*0 An converges only ifby converges
check to ensure buco
↳
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