Why-lim-n-x-n-u-n-0-When-u-n-is-bounded-

Question Number 204805 by York12 last updated on 27/Feb/24

Why \lim_{n \to \infty} (x^{n} u_{n}) = 0, When u_{n} is bounded

Commented by mr W last updated on 27/Feb/24

o n l y t r u e i f ∣ x ∣< 1 .

p r o o f :

w h e n ∣ x ∣< 1, \lim_{x \to \infty} x^{n} = 0

s a y a ⩽ u_{n} ⩽ b

{a x}^{n} ⩽ x^{n} u_{n} ⩽ {b x}^{n}

0 = \lim_{n \to \infty} {a x}^{n} ⩽ \lim_{n \to \infty} x^{n} u_{n} ⩽ \lim_{n \to \infty} {b x}^{n} = 0

\Rightarrow \lim_{n \to \infty} x^{n} u_{n} = 0

Commented by justenspi last updated on 27/Feb/24

Thank you sir may I a s k f o r analysis or calculud

book recommendation

Commented by justenspi last updated on 27/Feb/24

t h a n k y o u

Commented by mr W last updated on 28/Feb/24

s o r r y, i k n o w n o b o o k w h i c h i c a n

r e c o m m e n d .

Commented by York12 last updated on 28/Feb/24

thank you .

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