/sci/ - Science & Math

>>9644570
Please don't rub salt in the wound

how do I show [math]x_{n} = \frac{1}{2^{n}}[/math] is cauchy using the definition:

[math]\forall \hspace{0.2cm} \epsilon > 0\hspace{0.2cm} \exists\hspace{0.2cm} N \in \mathbb{N}\hspace{0.2cm} \text{such that}\hspace{0.2cm} \forall\hspace{0.2cm} m,n \geq N, |x_{n}-x_{m}| < \epsilon [/math]

I get as far as [math]\big| \frac{1}{2^{n}} - \frac{1}{2^{m}} \big| = \big| \frac{2^{m}+2^{n}}{2^{n+m}} \big| [/math]

>>9212918
t-thanks
i'm trying to get better anon, this takes time.

>>9196683
fuck this question, it's so simple but my iq is too low. t-thanks for the quick response