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

Answer 1

Not sure if I understood your question. maybe you meant a series of functions. Suppose that, for each n you have a function f_n and, for every x in the domain of the functions f_n, you define S(x) = f_1(x) + ....f_n(x) +...provided this series converges. Then, you have a series of functions, since for every x S(x) is given by the limi of a series.

For example, consider s(x) = 1 + x x^2/(2!) ....+ x^n(n!)....|This is a power series, in this case it converges for every real x. This is the definitioj of the exponencial function e^x

Answer 2

A functionality is a map from an internet site set to a form set. The requirement is merely that each and every element of the area map uniquely to a value. confident, any sequence fulfills this requirement as a map from the organic numbers to three different set. %. an arithmatic series and take a examine out it: a million 3 5 7 9 11... f(a million) = a million f(2) = 3 f(3) = 5 f(4) = 7 ... What form of functionality is f? geometric: %. an occasion: 2, 6, 18, fifty 4 f(a million) = 2 f(2) = 6 f(3) = 18 ...

Answer 3

i think she meant "sequence" like a_n
In this case , yes, you can see the sequence as a function from N to R( if the sequence has real numbers)