Suppose that (an)n20 is a bounded sequence of real numbers. For each natural number n, define fn(x) = L k=0 Prove that for each r> 0, the sequence of functions (fn)n21 Converges uniformly to a function f on (-r, r].
Suppose that (an)n20 is a bounded sequence of real numbers. For each natural number n, define fn(x) = L k=0 Prove that for each r> 0, the sequence of functions (fn)n21 Converges uniformly to a function f on (-r, r].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![6. Suppose that (an)n>o is a bounded sequence of real numbers. For each natural number
n, define
n
fn(x) = k
k!
k=0
Prove that for each r > 0, the sequence of functions (fn)n>1 converges uniformly to a
function f on [-r, r].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf1ba2d0-2c99-4364-8bc9-d4a1b82f85ab%2F2ede39d5-d54e-4843-bc69-2f4bde76b129%2Fy9e5ia_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Suppose that (an)n>o is a bounded sequence of real numbers. For each natural number
n, define
n
fn(x) = k
k!
k=0
Prove that for each r > 0, the sequence of functions (fn)n>1 converges uniformly to a
function f on [-r, r].
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