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If-I-n-0-1-1-x-4-n-dx-and-I-n-I-n-1-n-n-1-then-find-




Question Number 200930 by Spillover last updated on 26/Nov/23
If I_n =∫_0 ^1 (1−x^4 )^n dx  and  (I_n /I_(n−1) )=((λn)/(λn+1))  then find  λ
$${If}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{4}} \right)^{{n}} {dx}\:\:{and}\:\:\frac{{I}_{{n}} }{{I}_{{n}−\mathrm{1}} }=\frac{\lambda{n}}{\lambda{n}+\mathrm{1}} \\ $$$${then}\:{find}\:\:\lambda \\ $$
Commented by mr W last updated on 26/Nov/23
i think it′s wrong. (I_n /I_(n−1) ) can not be  written as ((λn)/(λn+1)).
$${i}\:{think}\:{it}'{s}\:{wrong}.\:\frac{{I}_{{n}} }{{I}_{{n}−\mathrm{1}} }\:{can}\:{not}\:{be} \\ $$$${written}\:{as}\:\frac{\lambda{n}}{\lambda{n}+\mathrm{1}}. \\ $$

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