Write the value of lim X - n - n -1 - n -1 - n -2 -

Lim_x →∞n! + (n +1)!/(n + 1) ! + (n +2) ! = lim_x →∞n![1 + n + 1]/(n+1) ! [1 + n + 2] = lim_x →∞(n + 2)/(n + 1 ) (n + 3) = lim_x →∞(1/n+ 2/n^2 )/(1+ 1/n ) ( ...

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Standard XII

Mathematics

Evaluation of Limit

Write the val...

Question

Write the value of ${lim}_{x \to \infty} \frac{n! + (n + 1)!}{(n + 1)! + (n + 2)!}$

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Solution

${lim}_{x \to \infty} \frac{n! + (n + 1)!}{(n + 1)! + (n + 2)!} = {lim}_{x \to \infty} \frac{n! [1 + n + 1]}{(n + 1)! [1 + n + 2]} = {lim}_{x \to \infty} \frac{(n + 2)}{(n + 1) (n + 3)} = {lim}_{x \to \infty} \frac{(\frac{1}{n} + \frac{2}{n^{2}})}{(1 + \frac{1}{n}) (1 + \frac{3}{n})} = \frac{0}{1 \times 1} = 0 = {lim}_{x \to \infty} \frac{n! + (n + 1)!}{(n + 1)! + (n + 2)!} = 0$

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Write the value of limx→∞n!+(n+1)!(n+1)!+(n+2)!

limx→∞n!+(n+1)!(n+1)!+(n+2)!=limx→∞n![1+n+1](n+1)![1+n+2]=limx→∞(n+2)(n+1)(n+3)=limx→∞(1n+2n2)(1+1n)(1+3n)=01×1=0=limx→∞n!+(n+1)!(n+1)!+(n+2)!=0

Write the value of ${lim}_{x \to \infty} \frac{n! + (n + 1)!}{(n + 1)! + (n + 2)!}$