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[tex] x_{n}+px_{n-1} [/tex] converges [tex]\Leftrightarrow x_{n}[/tex] converges.
For which p it is true?
Thanks
Final
For which p it is true?
Thanks
Final
Final said:[tex] x_{n}+px_{n-1} [/tex] converges [tex]\Leftrightarrow x_{n}[/tex] converges.
For which p it is true?
Thanks
Final
learningphysics said:...
Assume [tex]y_{n}[/tex] converges. So there is a finite M such that:
[tex]\lim_{n \rightarrow \infty} x_{n} + px_{n-1} = M[/tex]
we can rewrite the left side:
[tex]\lim_{n \rightarrow \infty} x_{n} + p \lim_{n \rightarrow \infty} x_{n-1} = M[/tex]
...
Muzza said:That's only true if x_n converges, which is what you were trying to prove... ;)
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