Does the Existence of a Sequence Imply the Existence of a Derivative?

[kbfrob]

Homework Statement

If f: R->R is differentiable at c in R, show that:
f'(c)=lim(n{f(c+1/n)-f(c)})

Show by example that the existence of this sequence doesn't imply the existence of f'(c)

The Attempt at a Solution

I got the second part, with my example just being |x|, but I'm not sure about the first part.

 

[e(ho0n3]

I assume the limit is to be taken as n -> infinity. Do you know the standard definition of the derivative of f at c? Can you take the definition in your problem and somehow change it to match the standard definition?

 

[rochfor1]

Show the work you've done, and think about the sequential criterion for limits.