5.1 The ratio decides the geometric tail · Sequences and Series, First Half · Visual Calculus

5.1Geometric sequences

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5.1Epsilon band 5.1Geometric sequences 5.1Squeeze theorem 5.1Monotone + bounded 5.1Cobweb recurrence 5.2Partial sums 5.2Geometric series 5.2Telescoping series 5.2Harmonic series 5.3Divergence test 5.3Integral test 5.3p-series 5.3Remainder estimate

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Home Calculus IISections 5.1-5.35.1 The ratio decides the geometric tail

5.1

The ratio decides the geometric tail

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SymPy check = 0

SymPy checks

Limit of epsilon-band sequence1

Limit of geometric sequence0

Squeezed sequence limit0

Monotone bounded sequence limit0

Positive fixed point of recurrence1

Oil-seepage geometric sum2

Alternating geometric sum5.1428571429

Telescoping series sum1

Convergent p-series contrast1.6449340668

Divergence-test term limit0.3333333333

Integral-test p=2 tail1

p-series tail integral at p=40.3333333333

Remainder upper bound at N=100.005