Our minds are finite, and yet even in these circumstances of finitude we are surrounded by possibilities that are infinite, and the purpose of life is to grasp as much as we can out of that infinitude.

Alfred North Whitehead

sections:

      9.1, 9.2, 9.3, 9.4, 9.5, 9.6, 9.7, 9.8, 9.9, and 9.10

The material focuses on sequences and series.

objectives:

• define a sequence
• define a sequence with a closed formula
• describe a sequnece with a recurrence relation
• determine the convergence or divergence of a sequence
• find the limit of a sequence
• describe a monotonic sequence
• define a bounded sequence
• define a series
• describe the convergence or divergence of a series
• define a geometric series
• use the nth-term test for divergence of an infinite series
• apply the integral test
• define a p-series
• describe a harmonic series
• utilize properties of p-series and harmomic series
• apply the direct comparison test
• use the limit comparison test
• describe an alternatinf series
• compute the remainder of an alternating series
• approximate the the sum of an alternating series
• classify a convergent series as absolutely or conditionally convergent
• compute the remainder of an alternating series
• apply the ratio test
• use the root test
• apply approriate test for a given series
• define a Taylor polynomial
• find polynomial approximations
• compute the Taylor series
• calculate a Maclaurin series
• define a power series
• find the radius and interval of convergence of a power series
• determine the endpoint converges of a power series
• differentiate a power series
• integrate a power series
• represent functions by a power series
• describe operations with power series
• find a Taylor series for a given function
• find a Maclaurin series for a given function