Calc 2

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9 Terms

1

nth term divergence test

If limit is DNE or not equal to zero, the series diverges.

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2

p-series

if p > 1 series converges
if p <= 1 series diverges

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3

integral test

if integral converges series converges (equal a finite number)
if integral diverges series diverges

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4

limit comparison test

Limit an / bn = L
if L > 0 & bn converge, an converges, vice versa
if L = 0 & bn converge, an converge
if L = infinity & bn diverge, an diverge

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5

direct comparison test

if an <= bn and bn converges, then an converges; if an >= bn and bn diverges, then an diverges.

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6

ratio test

limit | an+1 / an | = L
L < 1, series converges
L > 1, series diverges
L = 1, test inconclusive.

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7

root test

limit | an^(1/n) | = L
L < 1, series converges
L > 1, series diverges
L = 1, test inconclusive.

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8

power series

f(x) + f’(x)(x - c) + f’’(x)/2! (x - c)² + f’’’(x)/3! (x-c)³

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9

integral of maclaurin or taylor

t^m+1 / m+1

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