Tedious Multiplication? - 2

Calculus Level 2

lim ⁡ n → ∞ ( 5 1 × 6 2 × ⋯ × n n − 4 ) = ? \large \displaystyle \lim_{n \to \infty} \left( \dfrac{5}{1} \times \dfrac{6}{2} \times \cdots \times \dfrac{ n}{ n -4} \right) =\, ?

Inspiration .

2 1 3 0 Not Defined

Harshit Mittal by Harshit Mittal , 23, India

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1 solution

Sabhrant Sachan
Jul 2, 2016

lim ⁡ n → ∞ ( ∏ r = 4 n − 1 r + 1 r − 3 ) = 1 24 lim ⁡ n → ∞ n ! ( n − 4 ) ! lim ⁡ n → ∞ n ( n − 1 ) ( n − 2 ) ( n − 3 ) 24 → ∞ \quad \displaystyle \lim_{n \to \infty} \left( \prod_{r=4}^{n-1} \dfrac{r+1}{r-3} \right) = \dfrac{1}{24} \displaystyle \lim_{n \to \infty} \dfrac{n!}{(n-4)!} \\ \quad \displaystyle \lim_{n \to \infty} \dfrac{n(n-1)(n-2)(n-3)}{24} \rightarrow \infty

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