CBC-Chp-11-3-NTs - CalcBC Chp 11-3 Integral test and...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
CalcBC Chp 11-3 Integral test and Estimate sum of a series NOTES 1. Sum of an infinite series Previously used partial sums to create a general term of partial sums, S n , such that the sum of the infinite series is . This method is helpful only for some series. Need other methods to determine convergence and sums of series. Other sections in this chapter will be showing other methods for other series. 2. GEOMETRIC SERIES Look for common ratio. The sum formula can be used if and only if the common ratio is | r | < 1. If the common ratio is r 1 or r 1, then the series diverges. 3. p-SERIES Look for the ratio as If p < 1, then the series diverges because it becomes If p = 1, the series diverges called a HARMONIC SERIES If p > 1, then the series CONVERGES The denominator grows fast while the numerator stays as one value, the series very quickly approaches insignificantly small amounts.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4. INTEGRAL TEST Determines a series' converge nce Given The gist is to convert a n to be f(n) and use IMPROPER INTEGRALS
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/21/2011 for the course MATH 408C taught by Professor Knopf during the Spring '10 term at University of Texas at Austin.

Page1 / 4

CBC-Chp-11-3-NTs - CalcBC Chp 11-3 Integral test and...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online