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can some kind soul tell me what is this question asking and how to solve it?

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- Jan 10th 2010, 07:37 AMalexandrabel90differentiable functions
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can some kind soul tell me what is this question asking and how to solve it? - Jan 10th 2010, 08:00 AMabender
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. - Jan 10th 2010, 08:05 AMalexandrabel90
may i know what does the LHS N look a like symbol from k=1 to n mean? this is the first time im seeing that symbol thats why.

- Jan 10th 2010, 08:16 AMabender
$\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 $ - Jan 10th 2010, 08:28 AMalexandrabel90
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this is how i have done it..but i got stuck as to how to continue from there.. - Jan 10th 2010, 08:30 AMVonNemo19
- Jan 10th 2010, 08:51 AMalexandrabel90
how do you show that A(n+1) = 0 from my working and hence the equation is true by induction?

- Jan 10th 2010, 10:04 AMabender