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Question Number 4943 by madscientist last updated on 25/Mar/16

1 whole ÷(1/4)=0.25÷(1/4)=0.0625÷(1/4)...∞  1 whole divided by (1/4) infinitly = what  how? what would the formula look like?

$$\mathrm{1}\:{whole}\:\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{4}}=\mathrm{0}.\mathrm{25}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{4}}=\mathrm{0}.\mathrm{0625}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{4}}...\infty \\ $$$$\mathrm{1}\:{whole}\:{divided}\:{by}\:\frac{\mathrm{1}}{\mathrm{4}}\:{infinitly}\:=\:{what} \\ $$$${how}?\:{what}\:{would}\:{the}\:{formula}\:{look}\:{like}? \\ $$

Commented by FilupSmith last updated on 25/Mar/16

1÷(1/4)≠0.25  1÷4=0.25    If you mean what is S=(((1÷4)÷4)÷4)÷...  ∴S=0    ∵((((((((a/b)))/b)/b)))/(...))=(a/b^k )  k→∞  ∴S=(a/b^∞ )  S = lim_(x→∞)  (a/x) = 0

$$\mathrm{1}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{4}}\neq\mathrm{0}.\mathrm{25} \\ $$$$\mathrm{1}\boldsymbol{\div}\mathrm{4}=\mathrm{0}.\mathrm{25} \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{what}\:\mathrm{is}\:{S}=\left(\left(\left(\mathrm{1}\boldsymbol{\div}\mathrm{4}\right)\boldsymbol{\div}\mathrm{4}\right)\boldsymbol{\div}\mathrm{4}\right)\boldsymbol{\div}... \\ $$$$\therefore{S}=\mathrm{0} \\ $$$$ \\ $$$$\because\frac{\left(\frac{\frac{\left(\frac{{a}}{{b}}\right)}{{b}}}{{b}}\right)}{...}=\frac{{a}}{{b}^{{k}} } \\ $$$${k}\rightarrow\infty \\ $$$$\therefore{S}=\frac{{a}}{{b}^{\infty} } \\ $$$${S}\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{a}}{{x}}\:=\:\mathrm{0} \\ $$

Answered by FilupSmith last updated on 25/Mar/16

(a/(((b/c))))=((ac)/b)   1÷(1/4)=4  4÷(1/4)=16  16÷(1/4)=64  ...    ∴ it diverges towards ∞

$$\frac{{a}}{\left(\frac{{b}}{{c}}\right)}=\frac{{ac}}{{b}} \\ $$$$\:\mathrm{1}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{4}}=\mathrm{4} \\ $$$$\mathrm{4}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{4}}=\mathrm{16} \\ $$$$\mathrm{16}\boldsymbol{\div}\frac{\mathrm{1}}{\mathrm{4}}=\mathrm{64} \\ $$$$... \\ $$$$ \\ $$$$\therefore\:\mathrm{it}\:\mathrm{diverges}\:\mathrm{towards}\:\infty \\ $$

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