Stitz-Zeager_College_Algebra_e-book

5 2 since 225 is negative we start at the positive x

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: g the summation using ‘n’ as the index. 566 Sequences and the Binomial Theorem If we rewrite the quantity 2a + (n − 1)d as a + (a + (n − 1)d) = a1 + an , we get the formula S=n a1 + an 2 A helpful way to remember this last formula is to recognize that we have expressed the sum as the product of the number of terms n and the average of the first and nth terms. To derive the formula for the geometric sum, we start with a geometric sequence ak = ark−1 , k ≥ 1, and let S once again denote the sum of the first n terms. Comparing S and rS , we get S = a + ar + ar2 + . . . + arn−2 + arn−1 rS = ar + ar2 + . . . + arn−2 + arn−1 + arn Subtracting the second equation from the first forces all of the terms except a and arn to cancel out and we get S − rS = a − arn . Factoring, we get S (1 − r) = a (1 − rn ). Assuming r = 1, we can divide both sides by the quantity (1 − r) to obtain S=a 1 − rn 1−r If we distribute a through the numerator, we get a − arn = a1 − an+1 which yields the formula S= a1 − an+1...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern