Discrete Math Notes:
Chapter 7: Recursion
7.3 Summatons
lower limit and is the upper limit of the summatbn.
Summaton notatbn, used to express the sum of terms in a numerical sequence
summatbn form,The expression i=1 expanded form, 1
closed form,a mathematial expression that expresses the value of the sum without summaton notatbn.
Overview:
Example of a change in variable in summation
Substitute k =j - 1
Substitute variable j back 16 16
17
k=0
j=0
Initial index: j = 1 Final index: j= 17 Summation term:
k=j-1=1-1=0 k=j-1 =17 -1=16 k=j-1j=k+1 2j-1=2(k+1)-1=2k
Captions ^
2. Substitute the initial index j = 1 into the expression for k to get the initial condition for k:k=j-1=1-1=0 3. The new sum has an initial index of k = 0 : =0. 4. Substitute the final index j = 17 into the expression for k to get the final condition for
5. The equality k = j -- 1 implies j = k + 1. Substitute the expression for j in the