Find the value of the limit of the sequence defined by 
.
Definitions:
Sleeping Pills
Medications designed to assist individuals in falling asleep or staying asleep.
Down Syndrome
A genetic disorder caused by the presence of an extra 21st chromosome, leading to distinctive physical features and varying degrees of intellectual disability.
Chromosome 21
A chromosome in humans that is associated with the physical and cognitive manifestations of Down syndrome when an individual has three copies.
Klinefelter Syndrome
A genetic condition where males have an extra X chromosome, leading to physical and cognitive development symptoms.
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