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Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Let _ n → ∞ n^ -(1)/(2)(1 + (1)/(n)) · (1^1 · 2^2 · 3^3 n^n)^...

Let

\lim_{n \to \infty} n^{-\frac{1}{2}\left(1 + \frac{1}{n}\right)} \cdot (1^1 \cdot 2^2 \cdot 3^3 \dots n^n)^{\frac{1}{n^2}} = e^{\frac{-p}{q}}

where

p

and

q

are relative prime positive integers. Find the value of

|p + q|

.

Correct answer

5

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