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Hint

1

partial sum

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2

geometric series

|r|<1 → convergent

|r|≥1 → divergent

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3

harmonic series

always divergent

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4

test for divergence

if the lim(a) DNE or lim(a)≠0 → the series is divergent

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5

integral test

only used if the function is continuous, positive, and decreasing

take the integral, then the limit

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6

p-series

p>1; convergent

p≤1; divergent

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7

remainder estimate for the integral test

where is f continuous, positive, and decreasing for x≥n and Σa is convergent

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8

comparison test

if Σa and Σb are series with positive terms

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9

limit comparison test

where c is positive and finite and Σa and Σb are series with positive terms

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10

alternating series

a series whose terms alternate from positive to negative

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11

alternating series test

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12

alternating series error bound theorem

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13

absolutely convergent

a series, Σa, is ______ if Σ|a| is convergent

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14

conditionally convergent

a series, Σa, is ______ if Σ|a| is divergent

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15

ratio test

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16

root test

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