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Alexeev081 [22]
3 years ago
12

Please

29%21%7D" id="TexFormula1" title=" \lim_{n \to \infty} \frac{(n+1)!}{n!-(n+1)!}" alt=" \lim_{n \to \infty} \frac{(n+1)!}{n!-(n+1)!}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Nana76 [90]3 years ago
3 0
Hi there!
We are given the function - 
\lim_{n \to \infty} \frac{(n+1)!}{n!-(n+1)!}
and are told to find the limit of the function. 
The limit would be n approaches infinity, giving us an answer of -1. 
Here is how you solve this:
\frac{(n+1)!}{n!-(n+1)!}
Divide by (n + 1)! - 
\frac{1}{\frac{1}{n+1}-1 }
Now, we can refine the function - 
\lim_{n \to \infty}\frac{1}{\frac{1}{n+1}-1 }
Now, just simplify. This gives us - 
\lim_{n \to \infty} (1)
We can use the rule \lim_{x \to a}c=c to simplify the whole thing to get 1. Finally, we plug it back into our second derived equation to get 1/-1, which simplifies to -1. Therefore, the answer is -1. Hope this helped and have a great day!


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Answer:

  • See attachment for table values
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Step-by-step explanation:

In each case, put the x-value in the formula and do the arithmetic. If you're allowed, you can save some time and effort by realizing that the solution (x) will have to be an even number.

y₁ is an integer value for all integer values of x. y₂ is an integer value for even values of x only. y₁ and y₂ will both be integers (and possibly equal) only when x is even.

For example, for x = 6, we have

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