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Previous: Changing Summation Limits
Next: Videos on Sigma Notation
Previous: Changing Summation Limits
Next: Videos on Sigma Notation
Change the following summation
so that the index of summation start at 1 instead of at 3.
Although not necessary, we will use two method for solving this problem: Method 1 and Method 2.
Introducing the transformation
so that when gives us
as desired.
Our procedure is to add and subtract terms in the sum to shift our index to 1:
as desired. Therefore
The transformation , was chosen to that the index would start at 1.
Most steps in this approach involved straightforward algebraic manipulation. Steps (3) and (5) involve adding and subtracting terms in a way that will allow us to change the summation limits.
More precicesly, in Step (3) we added and substracted the term, and in Step (5) we added and subtracted the term.
You may not have a choice. In some circumstances, you need to convert your sum in a way that does not change the general term.
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