Okay, where does it end?

Algebra Level 4

Y=[(1+1n)(1+2n)(1+3n)(1+nn)]1n \large\displaystyle Y= \left[ \left(1+\frac{1}{n}\right) \left(1+\frac{2}{n}\right) \left(1+\frac{3}{n}\right) \cdots \left(1+\frac{n}{n}\right) \right]^{\frac{1}{n}}

Find the value of Y\lceil Y \rceil, where nn is a positive integer.

Submit your answer as 123 if you think that the answer depends on the value of nn

Notation: \lceil \cdot \rceil denotes the ceiling function.

This problem is a part of the set All-Zebra


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