Sigma notation
(?1)k 1 k . Key Point. To write a sum in sigma notation try to find a formula involving a variable k where the first.
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INTRODUCTION TO SIGMA NOTATION 1. The notation itself Sigma
The variable k is called the index of the sum. The numbers at the top and bottom of the ? are called the upper and lower limits of the summation. In this case
1 Convergence Tests
Root Test and Ratio Test. The root test is used only if powers are involved. Root Test. ? k2. 2k converges: (ak). 1/k. =
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Feb 12 2006 b) P(k) ? P(k + 1) for all natural numbers k . The standard analogy to this involves a row of dominoes: if it is shown.
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Remarque : • La variable k est une variable muette c'est à dire qu'une fois la somme calculée le résultat ne dépend plus de k
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uk la somme de la série ?k?0 uk et on dit que la série est convergente Sinon on dit qu'elle est divergente Notations On peut noter une série de
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Le symbole ? (sigma) s'utilise pour désigner de manière générale la somme de plusieurs termes Ce symbole est généralement accompagné d'un indice que l'on
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1 Exercice 5 : Somme de termes en progression arithmétique — Soit (uk) une suite de nombres réels en progression arithmétique Soit(
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un changement où on inverse l'ordre d'énumération : on pose l = n ? k ?? k = n ? l Après un changement d'indice le nombre de termes dans la somme doit
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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 notation and establish some useful
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18 sept 2010 · Exemple 1 : Calcul de la somme des entiers • Nous allons démontrer par récurrence que la propriété Pn : i=n ?
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Déployer une somme Quand je parlerai de déployer une somme cela signi era qu'on récrit une somme initialement présentée avec le symbole sigma n ? k=1
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(Voir la correction ici) Calculer les sommes suivantes : 1 S = 10 ? k=1 k k=1 k2 9 D = n+2 ? k=5 k 10 E = 2n ? k=n k Exercice 2
INTRODUCTION TO SIGMA NOTATION
1.The notation itselfSigmanotation is a way of writing a sum of many terms, in a concise
form. A sum in sigma notation looks something like this: 5 X k=13k The (sigma) indicates that a sum is being taken. The variablek is called theindex of the sum. The numbers at the top and bottom of the are called theupperandlowerlimits of the summation. In this case, the upper limit is 5, and the lower limit is 1. The notation means that we will take every integer value ofkbetween 1 and 5 (so1, 2, 3, 4, and 5) and plug them each into the summand formula (here
that formula is 3k). Then those are all added together. 5 X k=13k= 31 + 32 + 33 + 34 + 35 = 45 Example 1.Write out what is meant by the following: 3 X k=01k+ 1 Here, the indexktakes the values 0, 1, 2, and 3. We'll plug those each into1k+1and add them together.
3 X k=01k+ 1=10 + 1 +11 + 1 +12 + 1 +13 + 1 Example 2.Write out what is meant by the following: 8 X i=1(1)iDate: Friday March 31, 2016. 12 INTRODUCTION TO SIGMA NOTATION
The index variable here is written asiinstead ofk. That's ok. The most common variables to use for indexes includei,j,k,m, andn. 8X i=1(1)i= (1)1+ (1)2+ (1)3+ (1)4+ (1)5+ (1)6+ (1)7+ (1)8 =1 + 1 +1 + 1 +1 + 1 +1 + 1 = 0Try one on your own.
Example 3.Write out what is meant by the following (no need to simplify): 4X n=1pn+ 1Let's try going the other way around.
Example 4.Write the following sum in sigma notation.2 + 4 + 6 + 8 +:::+ 22 + 24
Notice that we can factor a 2 out of each term to rewrite this sum as21 + 22 + 23 + 24 +:::+ 211 + 212
That means that we are adding together 2 times every number between1 and 12. The sigma notation could be
12X k=12k There is no need to usekas our index variable. We could have just as easily usedmorjinstead. 12X k=12k=12X m=12m=12X j=12jNotice, that these are NOT the same as
12X k=12m Example 5.Write the following sum in sigma notation. 112+14 18 +:::164 +1128
INTRODUCTION TO SIGMA NOTATION 3
This one is a little more complicated. We'll worry about the signs later, rst we'll deal with the numbers themselves. Do you notice a pattern in the terms? Sure, we get to the next term by dividing by 2.That is:
1 = 12 0=12 0 12 =12 1=12 1 14 =12 2=12 2 1128=12 7=12quotesdbs_dbs2.pdfusesText_2
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