help with limits

**pb6883** · September 26th 2009, 08:25 AM

hello

stuck on these two

a) limit of {[(-1)^n]/(n^3+1)^1/2}

and

b) limit of {3^n/(2^n_3^n}

both for n->plus infinity

**red_dog** · September 26th 2009, 08:43 AM

1) $\left|\frac{(-1)^n}{\sqrt{n^3+1}}\right|=\frac{1}{\sqrt{n^3+1}}\ to 0$ as $n\to\infty$ .

Then $\lim_{n\to\infty}\frac{(-1)^n}{\sqrt{n^3+1}}=0$

2) $\lim_{n\to\infty}\frac{3^n}{2^n-3^n}=\lim_{n\to\infty}\frac{3^n}{3^n\left[\left(\frac{2}{3}\right)^n-1\right]}=\lim_{n\to\infty}\frac{1}{\left(\frac{2}{3}\righ t)^n-1}=-1$

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