For each positive integer n, let yn=n1((n+1)(n+2)n+n˙)n1For x∈Rlet [x]be the greatest integer less than or equal to x. If (lim)n→∞yn=L, then the value of [L]is ______.

Name: Video solution 1: For each positive integer n, let yn=n1((n+1)(n+2)n+n˙)n1For x∈Rlet [x]be the greatest integer less than or equal to x. If (lim)n→∞yn=L, then the value of [L]is ______.
Uploaded: 2021-01-01T18:41:02.000Z
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Description: Video solution 1: For each positive integer n, let yn=n1((n+1)(n+2)n+n˙)n1For x∈Rlet [x]be the greatest integer less than or equal to x. If (lim)n→∞yn=L, then the value of [L]is ______.

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For each positive integer $n$ , let $y_{n} = \frac{1}{n} ((n + 1) (n + 2) \dot{n + n})^{\frac{1}{n}}$ For $x \in R$ let $[x]$ be the greatest integer less than or equal to $x$ . If $(lim)_{n \to \infty} y_{n} = L$ , then the value of $[L]$ is ______.

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For each positive integer

n

, let

y_{n} = \frac{1}{n} ((n + 1) (n + 2) \dot{n + n})^{\frac{1}{n}}

For

x \in R

let

[x]

be the greatest integer less than or equal to

x

. If

(lim)_{n \to \infty} y_{n} = L

, then the value of

[L]

is ______.

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Question Text	For each positive integer $n$ , let $y_{n} = \frac{1}{n} ((n + 1) (n + 2) \dot{n + n})^{\frac{1}{n}}$ For $x \in R$ let $[x]$ be the greatest integer less than or equal to $x$ . If $(lim)_{n \to \infty} y_{n} = L$ , then the value of $[L]$ is ______.
Answer Type	Video solution: 1
Upvotes	151

For each positive integer n, let yn​=n1​((n+1)(n+2)n+n˙​)n1​For x∈Rlet [x]be the greatest integer less than or equal to x. If (lim)n→∞​yn​=L, then the value of [L]is ______.

Filo tutor solutions (1)

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For each positive integer $n$ , let $y_{n} = \frac{1}{n} ((n + 1) (n + 2) \dot{n + n})^{\frac{1}{n}}$ For $x \in R$ let $[x]$ be the greatest integer less than or equal to $x$ . If $(lim)_{n \to \infty} y_{n} = L$ , then the value of $[L]$ is ______.