sigma math exercice

Exercises: 1 Write out each of the following sums (a) X6 n=1 n4 (b) X7 k=3 k + 1 k (c) Xn i=2 (2i 1) (d) Xn k=0 2k+1xk (e) n k=0 ( k1) xk 2k + 1 2 Express each of these sums using sigma notation (a)1 + 4 + 9 + 16 + 25 + 36 (b)3 5 + 7 9 + 11 13 + 15 (c) 1 2 + 1 5 + 8 + 1 11 + 14 + 17 (d) 2 3 + 3 4 + 4 5 + + n+1 n+2 (e)2 22 + 23 24 + + 22n+1 (f

Chapter 1 Sigma-Algebras 1 1 De nition Consider a set X A {algebra F of subsets of X is a collection the following conditions: F of subsets of X satisfying (a) ; 2 F (b) if B 2 F (c) if B1; B2; ::: then its complement Bc is also in F is a countable collection of sets in F then their union [1 n=1Bn

1 Introduction Sigma notation is used as a convenient shorthand notation for the summation of terms For example: 5 1 We write X n = 1 + 2 + 3 + 4 + 5 n=1 Here the symbol P (sigma) indicates a sum The variable n is called the index and increments by 1 with each iteration The numbers at the top and bottom of the sigma are called upper and

Exercise 0 1 Show that the sum of rst n positive integer is given by Xn i=1 i = Exercise 0 2 Write the following in sigma notation and evaluate the summations 1

Sigma notation mc-bus-sigma-2009-1 Introduction Sigma notation P provides a concise and convenient way of writing long sums This leaflet explains how Sigmanotation The sum 1+2+3+4+5+ +10+11+12 can be written very concisely using the capital Greek letter P as kX=12 k=1 k The P

Introduction Sigma notation is a concise and convenient way to represent long sums For example we often wish to sum a number of terms such as 1 + 2 + 3 + 4 + 5 or 1 + 4 + 9 + 16 + 25 + 36 where there is an obvious pattern to the numbers involved