Mathematics · Sequences and Series
Let fn: (0, 1) → ℝ be defined as fn(x) = nnx + 1. Select the INCORRECT statement among the following:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1{fn(x)} converges pointwise to the limit function 1/x on (0, 1).
- 2fn(x) ≤ fn+1(x) for every n and x ∈ (0, 1).
- 3{fn(x)} converges uniformly on (0, 1).✓
- 4{fn(x)} converges uniformly on [a, 1) where 0 < a < 1.
Correct answer
{fn(x)} converges uniformly on (0, 1).
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