A. MATHconcept Check. Fill in the blank(s).

1. A _________ is a function whose domain is a subset of all positive integers and whose range is the set of all real numbers. The numbers in the range of a sequence function is called ________.

2. The sum of the elements of the sequence is called _________. Moreover, given the sequence , the expression _____________________ is called a series.

3. __________ can be defined by the equation where = ∑ () = () + ( + 1) + ( + 2) + ( + 3) + … + () _____________ and _________________ are integers and ___________.

4. If the given sequence defined by and , then 1 = 2 = 2−1 2 9 = _____________

5. The sigma notation of exercise #4 is ___________where the lower limit is 0 and the upper limit is .

6. ______________ is a statement , involving the positive integer , is true for all positive integer values of if the two conditions are satisfied:

7. ___________ is true; that is the statement is true for = 1.

8. If _____________ is an arbitrary ___________ integer for which is true, then is also _________ true; that is, whenever the true statement is true for ________, it is also true for ___________, where is an arbitrary positive integer.​