Science Quiz / Series Tests

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Can you name the Series?

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SequenceSeries TestConverges if...
athe limit (as n->inf) of |next term / first term| < 1
first term - next termthe limit (as n->inf) of the first term exists
a(r^n)|r| < 1, diverges if |r| >= 1
a0 < a =< b, and the summation of b from n=1 to inf. converges
a * (-1)^nnext term < first term, and the limit (as n->inf) of a is 0
athe limit (as n->inf) of the nth root of |a(n)| < 1
athe 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
aCannot show convergence, but can show divergence
1 / (n^p)p > 1, diverges p

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