please help with this question..
First, it is given that f(x) is a differentiable function.
and
Then, I have to prove by MI that
I don' t understand how to prove it . please help~
Do this like this.Originally Posted by ling_c_0202
Proof (by induction) that,
=
Then,
Then by the theorem before the derivative is,
- n times. But each summand can be reduced to, n-times. Thus,
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Keep you Calculus question in Calculus section
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The above is the base case for the induction with .Originally Posted by ling_c_0202
Suppose this is true for some , thenThen, I have to prove by MI that
Now (using the product rule):
So applying the supposition to the first term:
Which is the required result for .
So if we assume the required result for some , it is true for , hence
with the base case the result is proven by Mathematical Induction for all
(note we could have taken as the base case - which is trivialy true -
then the proof would apply for all ).
RonL