Auto-inflating series

[Richard Mayo]

I say chaps,
    I need to generate a series expression, like a Fourier series, but 
with a finite number of terms, that number being an integer variable. 
Coefficients within each term will also be variables, but that's not the 
problem.
It sounds like some string manipulation is called for, with a loop 
statement concatenating terms as required. Then I need to turn that 
string into an expression to be evaluated. How do I do that? All help 
gratefully received.

TTFN
    Richard.