May I Borrow Your Telescope?

Calculus Level 4

\[ \large \sum_{i=1}^{\infty} \frac{(-1)^i (i^2 + i + 1)}{i!} =\, ?\]

\[\] Notation: \(!\) is the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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