Instructions

For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to the second decimal place; e.g. 6.25, 7.00, -0.33, -.30, 30.27, -127.30) using the mouse and the on-screen virtual numeric keypad in the place designated to enter the answer

Question 47

For each positive integer n, let
$$Y_{n} = \frac{1}{n}\left((n+1)(n+2).......(n+n)\right)^{\frac{1}{n}}$$
for $$x \in R$$, let [x] be the greatest integer less than or equal to x. If $$\lim_{n \rightarrow \infty} Y_{n} = L$$, then the value of [L] is ..........

Correct Answer: e

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For each positive integer n, let$$Y_{n} = \frac{1}{n}\left((n+1)(n+2).......(n+n)\right)^{\frac{1}{n}}$$for $$x \in R$$, let [x] be the greatest integer less than or equal to x. If $$\lim_{n \rightarrow \infty} Y_{n} = L$$, then the value of [L] is ..........

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For each positive integer n, let
$$Y_{n} = \frac{1}{n}\left((n+1)(n+2).......(n+n)\right)^{\frac{1}{n}}$$
for $$x \in R$$, let [x] be the greatest integer less than or equal to x. If $$\lim_{n \rightarrow \infty} Y_{n} = L$$, then the value of [L] is ..........