What is the rule for manipulating the boundaries of a summation?

1. How do you invert limits of summation?
2. How do you change the upper and lower limit of summation?

How do you invert limits of summation?

If you want to reverse the order of the terms, you need to write ∑ni=1ai=∑ni=1an+1−i.

How do you change the upper and lower limit of summation?

We transform the lower and upper bounds and the summation appropriately, expressing them in terms of n: i=−20 becomes n=20. i=0 becomes n=0. (1/3)i becomes (1/3)−n.