The product rule for two functions is given by
$\displaystyle (f \cdot g)' = f' \cdot g + f \cdot g\ $
Using induction, prove that for any $\displaystyle n\geq2 $ number of functions, the generalized product rule (given to you) holds.
Start with your base case. Assume. Work up.
$\displaystyle \mathbf{Z}^{+} $ represents the set of positive integers. 1, 2, 3, ...
$\displaystyle \mathbf{R} $ represents the set of real numbers.
1, 905, -763, 0.13244, 0, 2/5, anything that is real (read: not imaginary; no i)
$\displaystyle \sum $ represents "the sum of." So, $\displaystyle \sum_{k=1}^n x^k = x^1 + x^2 + x^3 + ... + x^n $
$\displaystyle \prod $ represents "the product of." So, $\displaystyle \prod_{k=1}^n x^k = x^1 \cdot x^2 \cdot x^3 \cdot ... \cdot x^n $