hello

I really troubled with the following questions:

[tex]\mbox{1. }\, u_n\, =\, \left(\dfrac{2n^3\, -\, 4n^2\, +\, 5}{10n^3\, +\, 100}\right)\, \cdot\, 2^{-n}[/tex]

[tex]\mbox{2. }\, w_n\, =\, \left(\dfrac{3n\, +\, 2}{4n^2\, +\, 8n\, +\, 5}\right)\, \cdot\, \left(\dfrac{(1\, -\, n)^3}{(14\, -\, 5n)^2}\right)[/tex]

[tex]\mbox{3. }\, e_n\, =\, \dfrac{2^n\, +\, 3^{n-1}\, +\, 5^{2n+2}}{4^{n-7}\, +\, 5^{2n}}[/tex]

[tex]\mbox{4. }\, b_n\, =\, \dfrac{\left(\frac{2}{3}\right)^n}{\left(\frac{1}{ 2}\right)^n\, +\, \left(\frac{9}{10}\right)^n}[/tex]

[tex]\mbox{5. }\, S_n\, =\, 4\, \sqrt{\strut n\, +\, 3\,}\, -\, \sqrt{\strut n\, -\, 1\,}\, -\, 5\, \sqrt{\strut n\, +\, 7\,}\, +\, 2\, \sqrt{\strut n\, -\, 3\,}[/tex]

I need to

find the limit of each sequence.

My main concrn is thos 3 last sequence.

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