Section10.2-SummingAnInfiniteSeries

Section10.2-SummingAnInfiniteSeries - Section10.2...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 10.2 Summing an Infinite Series
Background image of page 1

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

View Full Document Right Arrow Icon
Definition A series is the sum of the terms of an infinite sequence. A series can have a finite sum. 123 1 nn n n aa a a a a  
Background image of page 2
Example Consider: A bug crosses a room by jumping ½ the remaining distance with each jump.
Background image of page 3

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

View Full Document Right Arrow Icon
Example continued Distance covered: 1 11 1 1 1 1 1 ? 22 2 2 2 2 2 1 2 n n n dl l l l l       So a series, an infinite sum, can be finite. (intuitively)
Background image of page 4
Partial Sum Definition: 123 1 1 n ni n n i s aaaa a a  11 21 2 3123 sa a aa   Partial sums form a sequence, {s n }.
Background image of page 5

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

View Full Document Right Arrow Icon
Convergence of Series If {s n } is convergent, then is a real number, series is convergent, and (sum of series). Otherwise, the series is divergent. (Thus, series have two associated sequences. These are the sequence of terms, {a n }, and the sequence of partial sums, {s n }.) lim n n ss  n a 1 n n as
Background image of page 6
Geometric Series 12 3 1 1 nn n ar a ar ar ar ar    Geometric series are distinguished by having a common ratio, r, of subsequent terms.
Background image of page 7

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

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 20

Section10.2-SummingAnInfiniteSeries - Section10.2...

This preview shows document pages 1 - 8. Sign up to view the full document.

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