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1. Fix R € (0,1). Prove that ot" converges pointwise to f(t) = on S = [-R, R]. Hint: Fix RE (0, 1) and t = [-R, R]. Let sn(t) = tº + t² + ... + tn−¹. Prove that limn→∞o Sn (t) = ₁ by rewriting sn(t) as a certain fraction. ? Div RC (01) TT 1 TIL 100

1. Fix R € (0,1). Prove that ot" converges pointwise to f(t) = on S = [-R, R]. Hint: Fix RE (0, 1) and t = [-R, R]. Let sn(t) = tº + t² + ... + tn−¹. Prove that limn→∞o Sn (t) = ₁ by rewriting sn(t) as a certain fraction. ? Div RC (01) TT 1 TIL 100

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Real Analysis II
1. Fix R € (0,1). Prove that ot" converges pointwise to f(t) = on S = [-R, R]. Hint: Fix RE (0, 1) and t = [-R, R]. Let sn(t) = tº + t² + ... + t−¹. Prove that limn→∞o Sn (t) = ₁ by rewriting sn(t) as a certain fraction. ? :.. RC (0.1) TT 1 UIT 100
Transcribed Image Text:1. Fix R € (0,1). Prove that ot" converges pointwise to f(t) = on S = [-R, R]. Hint: Fix RE (0, 1) and t = [-R, R]. Let sn(t) = tº + t² + ... + t−¹. Prove that limn→∞o Sn (t) = ₁ by rewriting sn(t) as a certain fraction. ? :.. RC (0.1) TT 1 UIT 100
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