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Science Quiz
/ Series Tests
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Science
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Can you name the Series?
by
bc_calc_group
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Identify the series test that is described. Let's see if you know more than just ratio...
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Smallest-to-Largest Planets
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Sequence
Series Test
Converges if...
a
the limit (as n->inf) of |next term / first term| < 1
first term - next term
the limit (as n->inf) of the first term exists
a(r^n)
|r| < 1, diverges if |r| >= 1
a
0 < a =< b, and the summation of b from n=1 to inf. converges
a * (-1)^n
next term < first term, and the limit (as n->inf) of a is 0
a
the limit (as n->inf) of the nth root of |a(n)| < 1
a
the limit (as n->inf) of a/b > 0, and the summation of b from n=1 to inf. converges
f(n)
the integral of f(x) dx from 1 to inf. converges
a
Cannot show convergence, but can show divergence
1 / (n^p)
p > 1, diverges p
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