Question: a) Prove that k=1 sin(x/k2) converges uniformly on any bounded interval in R. b) Prove that k=0e-kx converges uniformly on any closed subinterval of (0,

a) Prove that ∑∞k=1 sin(x/k2) converges uniformly on any bounded interval in R.
b) Prove that ∑∞k=0e-kx converges uniformly on any closed subinterval of (0, ∞).

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