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s-i-1-2-i-2s-s-1-s-1-how-to-explain-it-and-how-to-judge-which-case-can-use-this-way-




Question Number 210788 by liuxinnan last updated on 19/Aug/24
s=Σ_(i=1) ^∞ 2^i   2s=s−1  s=1 ?   how to explain it  and how to judge which case can use this way
$${s}=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{2}^{{i}} \\ $$$$\mathrm{2}{s}={s}−\mathrm{1} \\ $$$${s}=\mathrm{1}\:? \\ $$$$\:{how}\:{to}\:{explain}\:{it} \\ $$$${and}\:{how}\:{to}\:{judge}\:{which}\:{case}\:{can}\:{use}\:{this}\:{way} \\ $$
Answered by Berbere last updated on 19/Aug/24
when You have eqation  the variable is in set  2s=s−1  have s∈R..?  R=]−∞,∞[  s=Σ_(i=1) ^∞ 2^i >2^n ;∀n∈N  s→∞∉R
$${when}\:{You}\:{have}\:{eqation} \\ $$$${the}\:{variable}\:{is}\:{in}\:{set} \\ $$$$\mathrm{2}{s}={s}−\mathrm{1}\:\:{have}\:{s}\in\mathbb{R}..? \\ $$$$\left.\mathbb{R}=\right]−\infty,\infty\left[\right. \\ $$$${s}=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{2}^{{i}} >\mathrm{2}^{{n}} ;\forall{n}\in\mathbb{N} \\ $$$${s}\rightarrow\infty\notin\mathbb{R} \\ $$$$ \\ $$
Commented by liuxinnan last updated on 20/Aug/24
thanks
$${thanks} \\ $$

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