Using the index of a series as the domain and the value of the series as the range, is a series a function?

Question

Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?

Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?

Give real-life examples of both arithmetic and geometric sequences and series. Explain how these examples might affect you personally.

Answer 1

Absolutely. The series
x - x^3/3! + x^5/5! - x^7/7! + ....... is equal to sin(x) and there are thousands of other examples.

As for the rest, you have to do your own homework. That's how you really learn math ☺


Doug

Answer 2

A function is a map from a domain set to a range set. The requirement is just that each element of the domain map uniquely to a value. Yes, any series fulfills this requirement as a map from the natural numbers to some other set.

Pick an arithmatic sequence and try it:

1 3 5 7 9 11...
f(1) = 1
f(2) = 3
f(3) = 5
f(4) = 7
...

What type of function is f?

geometric: pick an example: 2, 6, 18, 54
f(1) = 2
f(2) = 6
f(3) = 18
...