Example: bankruptcy
Arithmetic and geometricprogressions
•find the sum of a geometric series; •find the sum to infinity of a geometric series with common ratio |r| < 1. Contents 1. Sequences 2 2. Series 3 3. Arithmetic progressions 4 4. The sum of an arithmetic series 5 5. Geometric progressions 8 6. The sum of a geometric series 9 7. Convergence of geometric series 12 www.mathcentre.ac.uk 1 c ...
Tags:
Information
Domain:
Source:
Link to this page:
Documents from same domain
sigma - mathcentre.ac.uk
www.mathcentre.ac.ukSigma notation Sigma notation is a method used to write out a long sum in a concise way. In this unit we look at ways of using sigma …
Ratios
www.mathcentre.ac.uk1. Introduction A ratio is a way of comparing two or more similar quantities. Ratios can be used to compare costs, weights, sizes and other quantities.
The geometry of a circle - mathcentre.ac.uk
www.mathcentre.ac.ukThe geometry of a circle mc-TY-circles-2009-1 In this unit we find the equation of a circle, when we are told its centre and its radius. There are
evaluation of mathematics support centres - …
www.mathcentre.ac.uk3 Section 1: Executive Summary Mathematics Support Centres (MSCs) have been established at universities in the UK and in a number of other countries
Partial fractions - mathcentre.ac.uk
www.mathcentre.ac.ukPartial fractions mc-TY-partialfractions-2009-1 An algebraic fraction such as 3x+5 2x2 − 5x− 3 can often be broken down into simpler parts called partial fractions.
Percentages
www.mathcentre.ac.ukKey Point Percentage means ‘out of 100’, which means ‘divide by 100’. To change a fraction to a percentage, divide the numerator by the denominator and multiply by
Polynomial functions - Mathematics resources
www.mathcentre.ac.uk3. Graphs of polynomial functions We have met some of the basic polynomials already. For example, f(x) = 2is a constant function and f(x) = 2x+1 is a linear function.
Solving inequalities - Mathematics resources
www.mathcentre.ac.ukSolving inequalities mc-TY-inequalities-2009-1 Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤. To ‘solve’ an
mathcentrecommunityproject - Mathematics …
www.mathcentre.ac.ukmathcentrecommunityproject encouraging academics to share maths support resources AllmccpresourcesarereleasedunderaCreativeCommonslicence community …
7.7 The exponential form - Mathematics resources
www.mathcentre.ac.uk7.7 The exponential form Introduction In addition to the cartesian and polar forms of a complex number there is a third form in which a complex number may be written - the exponential form.
Related documents
Worksheet 1: Patterns, Sequences and Series Grade 12 ...
mathsatsharp.co.za8. An arithmetic and geometric series both have the same first term, a = 9. The fifth term of the arithmetic series is equal to the second term of the geometric series minus 1. The sum of first three terms of the geometric series is equal to the twenty-eighth term of the arithmetric series.
PRE-CALCULUS FORMULA BOOKLET - C-pp HS learning lab site
cpphslearninglab.weebly.comSEQUENCES AND SERIES THE nth TERM OF AN ARITHMETIC SEQUENCE an a1 (n 1)d SUM OF A FINITE ARITHMETIC SERIES ( ) 2 1n a a n S THE nth TERM OF A GEOMETRIC SEQUENCE 1 1 n an a r SUM OF A FINITE GEOMETRIC SERIES r a a r S n n 1 1 1 THEOREMS FOR LIMITS LIMIT OF A SUM n n n n n n n (a b ) alim b o f o f o f LIMIT OF A DIFFERENCE n …
SAT Math Must-Know Facts & Formulas Numbers, Sequences ...
www.erikthered.comGeometric Sequences: each term is equal to the previous term times r Sequence: t1, t1 ·r, t1 ·r2, ... Example: r = 2 and t1 = 3 gives the sequence 3, 6, 12, 24, ... Factors: the factors of a number divide into that number without a remainder Example: the factors of 52 are 1, 2, 4, 13, 26, and 52
The Golden Ratio and the Fibonacci Sequence
www.math.ksu.eduIs the Fibonacci sequence a geometric sequence? Lets examine the ratios for the Fibonacci sequence: 1 1 2 1 3 2 5 3 8 5 13 8 21 13 34 21 55 34 89 55 ... Golden Ratio from other sequences Example. Next, start with any two numbers and form a recursive sequence by adding consecutive numbers. See what
Geometric Sequences - Alamo Colleges District
www.alamo.eduGeometric Sequences . Another simple way of generating a sequence is to start with a number “a” and repeatedly multiply it by a fixed nonzero constant “r”.This …
INFINITE SERIES
samagra.kite.kerala.gov.inhus , for infinite geometric progression a, ar, ar2, ..., if numerical value of common ratio r is less than 1, then S n = (1) 1 arn r − − 11 a arn rr − −− n this case, rn → 0 as n→∞ since | 1r < and then 0 1 arn r → −. herefore, n 1 a S r → − as n→∞. Smbolicall , sum to infinit of infinite geometric series is denoted ...
The Weierstrass Function - University of California, Berkeley
math.berkeley.eduThe Weierstrass Function Math 104 Proof of Theorem. Since jancos(bnˇx)j an for all x2R and P 1 n=0 a n converges, the series converges uni- formly by the Weierstrass M-test. Moreover, since the partial sums are continuous (as nite sums of continuous