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posted by  Part. Diff. Equat on 10/10/2008 9:57:35 AM  |  status: Live  

Prove series converges uniformly. Hint & formula to do to the problem provided

Course Textbook Chapter Problem
Other An Introduction to Analysis, 3rd e, William R. Wade, 0131453335 7.2 7
Question Details:
HINT: Use Abel's Formula (formula provided below)

Question: 
If  converges uniformly on a set R and if is bounded on E with  for all  and N , prove that converges uniformly on E. 

***************************************************************
ABEL'S FORMULA
Let  and   be real sequences, and for each pair of integers  set 
.
Then
for all integers . 
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