someone111888
New member
- Joined
- Dec 17, 2017
- Messages
- 2
hello
I really troubled with the following questions:
\(\displaystyle \mbox{1. }\, u_n\, =\, \left(\dfrac{2n^3\, -\, 4n^2\, +\, 5}{10n^3\, +\, 100}\right)\, \cdot\, 2^{-n}\)
\(\displaystyle \mbox{2. }\, w_n\, =\, \left(\dfrac{3n\, +\, 2}{4n^2\, +\, 8n\, +\, 5}\right)\, \cdot\, \left(\dfrac{(1\, -\, n)^3}{(14\, -\, 5n)^2}\right)\)
\(\displaystyle \mbox{3. }\, e_n\, =\, \dfrac{2^n\, +\, 3^{n-1}\, +\, 5^{2n+2}}{4^{n-7}\, +\, 5^{2n}}\)
\(\displaystyle \mbox{4. }\, b_n\, =\, \dfrac{\left(\frac{2}{3}\right)^n}{\left(\frac{1}{2}\right)^n\, +\, \left(\frac{9}{10}\right)^n}\)
\(\displaystyle \mbox{5. }\, S_n\, =\, 4\, \sqrt{\strut n\, +\, 3\,}\, -\, \sqrt{\strut n\, -\, 1\,}\, -\, 5\, \sqrt{\strut n\, +\, 7\,}\, +\, 2\, \sqrt{\strut n\, -\, 3\,}\)
I need to find the limit of each sequence.
My main concrn is thos 3 last sequence.
I really troubled with the following questions:
\(\displaystyle \mbox{1. }\, u_n\, =\, \left(\dfrac{2n^3\, -\, 4n^2\, +\, 5}{10n^3\, +\, 100}\right)\, \cdot\, 2^{-n}\)
\(\displaystyle \mbox{2. }\, w_n\, =\, \left(\dfrac{3n\, +\, 2}{4n^2\, +\, 8n\, +\, 5}\right)\, \cdot\, \left(\dfrac{(1\, -\, n)^3}{(14\, -\, 5n)^2}\right)\)
\(\displaystyle \mbox{3. }\, e_n\, =\, \dfrac{2^n\, +\, 3^{n-1}\, +\, 5^{2n+2}}{4^{n-7}\, +\, 5^{2n}}\)
\(\displaystyle \mbox{4. }\, b_n\, =\, \dfrac{\left(\frac{2}{3}\right)^n}{\left(\frac{1}{2}\right)^n\, +\, \left(\frac{9}{10}\right)^n}\)
\(\displaystyle \mbox{5. }\, S_n\, =\, 4\, \sqrt{\strut n\, +\, 3\,}\, -\, \sqrt{\strut n\, -\, 1\,}\, -\, 5\, \sqrt{\strut n\, +\, 7\,}\, +\, 2\, \sqrt{\strut n\, -\, 3\,}\)
I need to find the limit of each sequence.
My main concrn is thos 3 last sequence.
Attachments
Last edited by a moderator: