Learning Guide Learning Guide

88 • Chapter 3: Finding Solutions⎛n−1∑ ⎜⎝− 3 (i + 1 2 )22 n 2 + 3 23i=02ni + 1 2n⎞⎟⎠Then take the limit as n goes to ∞.> Limit( %, n=infinity );⎛n−1∑3limn→∞ 2i=0⎜⎝− 3 2(i + 1 2 )2n 2 + 3 2ni + 1 2n⎞⎟⎠> value(%);38Now, observe that you can obtain the same result by using an integral.> Int(-2/3*x^2+x, x=0..3/2 );> value(%);∫ 3/2− 20 3 x2 + x dx38For more information on calculus with Maple, see chapter 6.The LinearAlgebra PackageIn linear algebra, a set of linearly independent vectors that generates thevector space is a basis. That is, you can uniquely express any element inthe vector space as a linear combination of the elements of the basis.A set of vectors {v 1 , v 2 , v 3 , . . . , v n } is linearly independent if and onlyif wheneverc 1 v 1 + c 2 v 2 + c 3 v 3 + · · · + c n v n = 0