Sequences and Limits

(a) $$lim_{n\rightarrow\infty}$$ ($$\sqrt{(n + a)(n + b)} - n)$$ where a, b > 0
(b)$$lim _{n\rightarrow\infty}$$ (n!)1/n2

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(a) $$lim_{n\rightarrow\infty}$$ ($$\sqrt{(n + a)(n + b)} - n)$$ where a, b > 0
Rationalize the numerator by multiplying both numerator and denominator by $\sqrt{n+ a)(n+b)}+ n$. Then divide both numerator and denominator by n.
[/quote](b)$$lim _{n\rightarrow\infty}$$ (n!)1/n2[/QUOTE]
If $y= (n!)^{1/n^2}$ then
$$ln(n)= \frac{ln(n!)}{n^2}= \frac{ln(2)}{n^2}+ \frac{ln(3)}{n^2}+ \cdot\cdot\cdot+ \frac{ln(n)}{n^2}$$.