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[DOC File]MATH 1220 Convergence Tests for Series (with key examples)
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For example, the teacher may choose to use technology to model annuities after the students have covered the work on geometric series rather than earlier in the unit when the modelling activities are grouped together. It may be helpful to revisit the use of technology in modelling financial situations when the financial applications of series are treated as a way of establishing clearer ...
what is a geometric sequence

[DOC File]Section 1 - University of Wisconsin–Madison
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A geometric series has the form , where “a” is some fixed scalar (real number). A series of this type will converge provided that (r(< 1, and the sum is . A proof of this result follows. Consider the kth partial sum, and “r” times the kth partial sum of the series. The difference between rSk and Sk is . Provided that r ( 1, we can divide by (r 1), to obtain . Since the only place that ...
sum of geometric series

Geometric Series Examples
Representing Function by Series. Example 7 illustrates the reason we are so concerned about the geometric series. When x was used in place of the constant, the right side became a polynomial expression that is equivalent to whenever. This expression is very powerful. It lets us describe a non-polynomial function as a polynomial function. As the figure shows, the partial sum, , of the ...
formula for geometric series

[DOC File]ARITHMETIC AND GEOMETRIC SEQUENCE WORD PROBLEM …
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Applications of Geometric Series. Example 7: Express as a ratio of integers. Solution: Note that we can write the given number as. This is a geometric series with . Note that . Also, for this series, a = 0.73. Thus, the number can be expressed as the following ratio. Tests For Non-Geometric Series. Most series are not geometric – that is, there is not a ratio r that you multiply each term to ...
geometric sequence examples

[DOC File]12 - Mira Costa High
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INFINITE GEOMETRIC SERIES: The sum of the terms of an infinite geometric sequence is an . infinite geometric series. For some geometric sequences, gets close to a specific number as n gets very large. For example, consider the infinite series . LIMIT OR SUM OF AN INFINITE GEOMETRIC SERIES. When the limit or sum of an infinite geometric series is given by. MATHEMATICAL INDUCTION. skip ...
geometric series formula sum

[DOC File]Sequences and Series**
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ARITHMETIC AND GEOMETRIC SEQUENCE WORD PROBLEM EXAMPLES. A recovering heart attack patient is told to get on a regular walking program. The patient is told to walk a distance of 5 km the first week, 8 km the second week, 11 km the third week and so on for a period of 10 weeks. At that point the patient is to maintain the distance walked during the 10th week. How far will the patient walk ...
geometric sum formula

[DOC File]CHAPTER 7: SEQUENCES, SERIES, AND COMBINATORICS
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Geometric Series: THIS is our model series A geometric series converges for . Note: If the series converges, the sum of the series is . Example: The series converges with and . The sum of the series is 35. Integral Test: If f is a continuous, positive, decreasing function on with , then the series converges if and only if the improper integral converges. p-series: The series is convergent for ...
geometric sums

[DOC File]Section 1 - Radford
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A geometric series with first term 1, common ratio x, and n terms is the following. The sum of these terms is ( Key idea. We can accumulate a desired amount of money in a savings account by a fixed date by making regular deposits at regular intervalsa sinking fund. With a uniform deposit of d dollars at the end of each interval, and an interest rate of i per interval, the savings formula ...
what is a geometric series

[DOC File]Notes for COT 5405 - CS Department
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2010-04-21 · The sum of the first n terms of a geometric series with common ratio r ( 1 is: Example 5. Find the sum of a geometric series. Find the sum of the geometric series . a1 = 3(4)1(1 = __3_ Identify first term. r = __4__ Identify common ratio. Write rule for S13. _____= _67,108,863_ Substitute and simplify. Checkpoin. t . Find the sum of the ...
what is a geometric sequence

[DOC File]Chapter 2: Sequences and Series
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Geometric Series: Common Ratio (r): where r ≠ 1. Example: Given a geometric sequence with the first term 2 and a common ratio of 3, which term in the sequence is equal to 192? Infinite Geometric Series: If | r | < 1,then the series has a finite sum and the terms successively approach 0. We can determine this sum by using the formula for a finite geometric sequence and taking its limit as n ...
sum of geometric series

Geometric series example