136.271
Assignment 3: Section 9.8 and Uniform Convergence
(Due April 7 in class)
Note: show your work; a naked final answer is not worth anything.
1.
(a) Use the binomial series to expand 
. Simplify your
answer.
(b) Use part (a) to find the sum of the series 
. (No marks if other methods are used.)
2. Given the
sequence of functions 
find the
pointwise limit 
and then show
that the sequence 
converges
uniformly to 
.
(a) 
over the interval [0,1].
(b) 
over the interval [1,2].
3. Given the
sequence of functions 
find the
pointwise limit 
and then show
that the sequence 
does NOT converge uniformly to 
.
(a)
over the interval 
(b) 
over the interval [0,1].