MCQ
Evaluate: $\lim_{\text{n} \rightarrow \infty} \dfrac{\text{n}!}{(\text{n}+1)!-\text{n}!}$
- A0
- B1
- C2
- D3
Solution:
We have,$\lim\limits_{\text{n} \rightarrow \infty} \dfrac{\text{n}!}{(\text{n}+1)!-\text{n}!}$
$=\lim\limits_{\text{n} \rightarrow \infty} \dfrac{\text{n}!}{(\text{n}+1)\text{n}!-\text{n}!}$
$ =\lim\limits_{\text{n}\rightarrow \infty} \dfrac{1}{\text{n}+1-1}$
$ =\lim\limits_{\text{n}\rightarrow \infty}\frac{1}{\text{n}}=0$
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The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is:
|z1 + z2| = |z1| + |z2| is possible if:
$\text{z}_2=\bar{\text{z}_1}$
$\text{z}_2=\frac{1}{\text{z}_1}$
$\arg(\text{z}_1)=\arg(\text{z}_2)$
$|\text{z}_1|=|\text{z}_2|$