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posted by  Part. Diff. Equat on 10/3/2008 2:24:35 AM  |  status: Live  

Prove Sequence converges uniformly. Hint & Notes provided

Course Textbook Chapter Problem
Other An Introduction to Analysis, 3rd e, William R. Wade, 0131453335 7.1 7.1a
Question Details:
QUESTION: For each n in N, define . Prove the sequence converges uniformly to the constant zero function. 


Hint/Notes: We are on the chapter Infinite series functions and currently talking about Uniform convergence of Sequences. 
We have spoken about the definition of Converge Pointwise, Converge Uniformly
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posted by Fourier Dude on 10/3/2008 11:54:13 AM  |  status: Live
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Given ε>0 we should show that
 
So we have
 
Thus if then we have convergence.
 
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