Question Number 210788 by liuxinnan last updated on 19/Aug/24
$${s}=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{2}^{{i}} \\ $$$$\mathrm{2}{s}={s}−\mathrm{1} \\ $$$${s}=\mathrm{1}\:? \\ $$$$\:{how}\:{to}\:{explain}\:{it} \\ $$$${and}\:{how}\:{to}\:{judge}\:{which}\:{case}\:{can}\:{use}\:{this}\:{way} \\ $$
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](Q210795.png)
$${when}\:{You}\:{have}\:{eqation} \\ $$$${the}\:{variable}\:{is}\:{in}\:{set} \\ $$$$\mathrm{2}{s}={s}−\mathrm{1}\:\:{have}\:{s}\in\mathbb{R}..? \\ $$$$\left.\mathbb{R}=\right]−\infty,\infty\left[\right. \\ $$$${s}=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{2}^{{i}} >\mathrm{2}^{{n}} ;\forall{n}\in\mathbb{N} \\ $$$${s}\rightarrow\infty\notin\mathbb{R} \\ $$$$ \\ $$
Commented by liuxinnan last updated on 20/Aug/24
$${thanks} \\ $$