Can I change the dummy index in the Sum?
Yes, you can. Here is the example formula
Name of index and range is not always from 1 or from 0, it can start from any number. Index is dummy name. The name is not important; you can put any name as long as they are consistent.
If we have a sequence of numbers then we can put index on the sequence such that , , , , , and
But you can also start the index from zero if you like such that
, , , , , and
Of course, the results are the same because actually they sum over the same sequence of numbers.
Preferable reference for this tutorial is
Teknomo, Kardi (2015) Summation Tutorial. http://people.revoledu.com/kardi/tutorial/BasicMath/Sum/