Let and . Show that as . [Hint:use the product rule and induction on n]

I am studying for an exam when i came across this problem in my notes. Any help would be appreciated.

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- Oct 18th 2010, 05:30 PMzebra2147Product Rule with limits
Let and . Show that as . [Hint:use the product rule and induction on n]

I am studying for an exam when i came across this problem in my notes. Any help would be appreciated. - Oct 19th 2010, 08:06 AMMauritzvdworm
What about x, is there not more structure?

In order to use induction we will need for the initial step

Then for the induction hypothesis we assume

for all

then

however the induction hypothesis holds for all , so we have

- Oct 19th 2010, 08:29 AMzebra2147
No, that's all that we are given with regards to x. But your explanation is very helpful. For some reason I couldn't out the induction process together with the product rule.