Partial Sum of Consecutive Integers

Does a natural number n exist such that 1+2+3+4+…+n is a three-digit number with identical digits?

(Adapted from Mathematics Teacher (1990). March Calendar; Problem 16, p207)

Extension:
Does a natural number n exist such that 1+2+3+4+…+n is a 4-digit, 5-digit, … number with identical digits?

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