Sigma Notation

Key Questions

  • How do you evaluate the sum represented by sum_(n=1)^5n/(2n+1) ?

    First expand the series for each value of n n/(2n+1)=1/(2(1)+1+2/(2(2)+1+3/(2(3)+1+4/(2(4)+1+5/(2(5)+1

    Next, perform the operations in the denominator...

    1/(3)+2/5+3/7+4/9+5/11

    Now, to add fractions we need a common denominator... in this case it's 3465

    Next, we have to multiply each numerator and denominator by the missing components...

    1/3 gets multiplied by 1155 giving 1155/3465

    (Divide the 3465 by 3 to get 1155 and divide the rest by the given denominator.)

    2/5*693/693=1386/3465, 3/7*495/495=1485/3465, 4/9*385/385=1540/3465 and 5/11*315/315=1575/3465

    Now simply add the numerators together... (1155+1386+1485+1540+1575)/3465

    giving 7141/3465.

    Lee E. · · Oct 13 2014
  • How do you use sigma notation to represent the series 1/2+1/4+1/8+…?

    1/2+1/4+1/8+cdots=1/2^1+1/2^2+1/2^3+cdots=sum_{n=1}^infty1/2^n

    Wataru · 1 · Sep 25 2014
  • How does sigma notation work?

    Sigma notation can be a bit daunting, but it's actually rather straightforward. The common way to write sigma notation is as follows:

    sum_(x)^nf(x)

    Breaking it down into its parts:

    • The sum sign just means "the sum".
    • The x at the bottom is our starting value for x. It usually has a number next to it: sum_(x=0), for example, means we start at x=0 and carry on upwards until we hit...
    • The n at the top.
    • The f(x) is what we need to plug all these values into. At the end, we add the results obtained from here together, and that's our answer.

    Note that it's not always f(x) - it is most often f(n) or f(i).

    As an example:

    sum_(x=0)^9(sqrt(x)+1)^2

    means we need to find

    (sqrt(0)+1)^2+(sqrt(1)+1)^2+(sqrt(2)+1)^2+...+(sqrt(9)+1)^2.

    CJ · 2 · Oct 14 2014

Questions

Introduction to Integration