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Stelistul07
Pe: 2012-12-02T13:10:31+02:00 In: In:

Siruri

Buna.. Sunt nou pe aici. Ma puteti ajuta si pe mine la cateva exercitii?
1.Sa se determine multimea limitelor subsirurilor urmatoarelor siruri:

    \[\begin{array}{l} a){a_n} = \frac{{{{( - 1)}^n}n}}{{n + 1}};\\ b){a_n} = 2\sin \frac{{n\pi }}{3};\\ c){a_n} = \sin \frac{{n\pi }}{3} + \cos \frac{{n\pi }}{6};\\ d){a_n} = {(\frac{{1 + i}}{{\sqrt 2 }})^n} + {(\frac{{1 - i}}{{\sqrt 2 }})^n} \end{array}\]

Apreciez orice ajutor! Merci.
P.S: Exercitii din lectia Proprietatea lui Weierstrass!

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5 raspunsuri

  1. PhantomR
    expert (VI)
  2. Stelistul07

    Mai are cineva vreo idee in privinta celorlalte puncte? Multumesc domnule PhantomR.

  4. PhantomR
    expert (VI)
  5. PhantomR
    expert (VI)

    4)

    Avem \frac{1+i}{\sqrt 2} = \frac{1}{\sqrt 2} + i \frac{1}{\sqrt 2} = \frac{\sqrt 2}{2} + i\frac{\sqrt 2}{2}= \cos \frac{\pi}{4}+i \sin \frac{\pi}{4}. La fel, \frac{1-i}{\sqrt 2} = \frac{1}{\sqrt 2}+i \frac{1}{\sqrt 2} = \frac{\sqrt 2}{2} + i \frac{\sqrt 2}{2}=\cos \frac{\pi}{4}-i\sin \frac{\pi}{4}.

    Acum a_n=\left( \cos \frac{\pi}{4}+i \sin \frac{\pi}{4}\right)^n+ \left(\cos \frac{\pi}{4}-i \sin \frac{\pi}{4} \right)^n= \cos \frac{n\pi}{4}+i \sin\frac{n\pi}{4}+\cos \frac{n\pi}{4}-i \sin \frac{n\pi}{4}=2\cos \frac{n\pi}{4}.

  6. ali
    maestru (V)

    b) periodicitatea este =6.
    c) periodicitatea este =12.

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