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Question Number 4950 by madscientist last updated on 25/Mar/16
what is a whole divided by diffrent amouts  infinitly what does it sooner or later equal?
$${what}\:{is}\:{a}\:{whole}\:{divided}\:{by}\:{diffrent}\:{amouts} \\ $$$${infinitly}\:{what}\:{does}\:{it}\:{sooner}\:{or}\:{later}\:{equal}? \\ $$
Commented by prakash jain last updated on 25/Mar/16
Successive division by 0<x<1  lim_(n→∞) (1/x^n )→∞  Successive division by 1 infinitely=1  Successive division by x >1 infinitely=0  succesive division x<−1=0  succesive division −1≤x≤0  indeterminate
$$\mathrm{Successive}\:\mathrm{division}\:\mathrm{by}\:\mathrm{0}<{x}<\mathrm{1} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{x}^{{n}} }\rightarrow\infty \\ $$$$\mathrm{Successive}\:\mathrm{division}\:\mathrm{by}\:\mathrm{1}\:\mathrm{infinitely}=\mathrm{1} \\ $$$$\mathrm{Successive}\:\mathrm{division}\:\mathrm{by}\:{x}\:>\mathrm{1}\:\mathrm{infinitely}=\mathrm{0} \\ $$$$\mathrm{succesive}\:\mathrm{division}\:{x}<−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{succesive}\:\mathrm{division}\:−\mathrm{1}\leqslant{x}\leqslant\mathrm{0}\:\:\mathrm{indeterminate} \\ $$

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