I'm trying to finish off my assignment (which is due tomorrow), and the last question asks me to do the following on Maple.
Write a procedure in Maple which calculates, in floating point form, the general term of the infinite series:
$$2 \space+\space 2.3x \space+\space 3.4x^2 \space+\space 4.5x^3 \space+\space ...$$
I have no problem finding the $n^{th}$ term of the series using Maple, or finding the sum of the series for some $x$ using Maple.
My problem is that "general term" used in the question.
Is it asking me to make a procedure that finds a term in the sum?
OR
Does it want me to write a procedure for the sum of the series for some $x$?
Take a series of the form $\sum\limits_{k=0}^\infty a_k x^k ~=~ a_0 x^0+a_1 x^1+a_2+\ldots + a_k+\ldots$ .
The term $a_k$ is the general term of the series. It is an expression for the $k$-th $0$-indexed term of the sequence, where $k$ is an arbitrary non-negative integer. $k\in\{0,1,2,\ldots\}$
In this case you are looking for the term $a_k x^k$ in the series $2+2.3x+3.4x^2+4.5x^3+\ldots$