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Author: Tinku Tara

Question-224432

Question Number 224432 by mr W last updated on 10/Sep/25 Commented by mr W last updated on 11/Sep/25 $${if}\:{an}\:{object}\:{takes}\:{the}\:{same}\:{time}\:{to} \\ $$$${reach}\:{the}\:{bottom}\:{of}\:{a}\:{bowl},\:{no}\: \\ $$$${matter}\:{at}\:{which}\:{point}\:{it}\:{is}\:{released} \\ $$$${on}\:{the}\:{interior}\:{of}\:{the}\:{bowl},\:{find}\:{the}…

lt-a-lt-b-lt-and-0-lt-lt-1-x-1-a-x-2-b-x-n-2-x-n-1-x-n-1-n-N-find-x-n-

Question Number 224392 by infinityaction last updated on 07/Sep/25 $$\:\:\:\:\:\:\:−\infty<{a}<{b}<\infty\:\:{and}\:\mathrm{0}<\lambda<\mathrm{1}\:\: \\ $$$$\:\:\:\:\:\:\:{x}_{\mathrm{1}} \:=\:{a}\:,\:{x}_{\mathrm{2}} \:=\:{b} \\ $$$$\:\:\:\:\:\:\:\:{x}_{{n}+\mathrm{2}} \:=\:\lambda{x}_{{n}} \:+\:\left(\mathrm{1}−\lambda\right){x}_{{n}+\mathrm{1}} \:\:\forall\:{n}\:\in\:\mathbb{N} \\ $$$$\:\:\mathrm{find}\:\:{x}_{{n}\:} \:=\:?\: \\ $$$$\:\:\:\:\:\:\:\:\:\: \\…