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
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
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
Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79599c56-a340-49a0-b0ff-829b3947a798%2F66802e53-3e6e-48a9-95e3-cc7071e19b66%2Fu7g9zke_processed.jpeg&w=3840&q=75)
