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December 17th, 2017, 07:42 AM   #1
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help with limits of sequences

Hello

I really troubled with the following questions

$\displaystyle u_n = \left(\frac{2n^3 - 4n^2 + 5}{10n^3 + 100}\right)\cdot2^{-n}$

$\displaystyle w_n = \left(\frac{3n + 2}{4n^2 + 8n + 5}\right)\cdot\left(\frac{(1 - n)^3}{(14 - 5n)^2}\right)$

$\displaystyle e_n = \frac{2^n + 3^{n - 1} + 5^{2n + 2}}{4^{n - 7} + 5^{2n}}$

$\displaystyle b_n = \frac{\left(\frac23\right)^n}{\left(\frac12\right) ^n + \left(\frac{9}{10}\right)^n}$

$\displaystyle S_n = 4\sqrt{n + 3} - \sqrt{n - 1} - 5\sqrt{n + 7} + 2\sqrt{n- 3}$

http://www.interload.co.il/upload/8256588.png

I need to calculate the limit of each sequence

My main concern is the last 3.

Last edited by skipjack; March 21st, 2018 at 12:08 PM.
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February 20th, 2018, 10:20 PM   #2
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The first expression has a limit of zero, but would have a limit of 1/5 if the $2^{-n}$ weren't present.

For the second limit, work out the terms in $n^4$, then divide the numerator and denominator by $n^4$.

For the third limit, divide the numerator and denominator by $5^{2n}$.

Last edited by skipjack; March 21st, 2018 at 12:58 PM.
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