AP EAMCET · Maths · Permutation Combination
For \(k > 0, \sum_{x=0}^{\infty} \frac{k^x}{x !} \lim _{n \rightarrow \infty} \frac{n !}{(n-x) !}\left(1-\frac{k}{n}\right)^{n-x}\left(\frac{1}{n}\right)^x=\)
- A 0
- B \(k\)
- C \(x\)
- D 1
Answer & Solution
Correct Answer
(D) 1
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {For } k > 0, \sum_{x=0}^{\infty} \frac{k^x}{x !} \lim _{n \rightarrow \infty} \frac{n !}{(n-x) !}\left(1-\frac{k}{n}\right)^{n-x}\left(\frac{1}{n}\right)^x \\ & =\lim _{n \rightarrow \infty} \sum_{x=0}^n \frac{n !}{x !(n-x)…
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