That's Too Many Terms To Write!

Algebra Level 1

Consider an arithmetic progression whose first term and common difference are both 100. If the nthn^\text{th} term of this progression is equal to 100!100!, find n.n.

Notation: !! denotes the factorial notation. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .

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