Show that 1 1 2n n 1 2 . Hint: For n 2, 1 1 2n n 1 1+1/(2n 1)n 1 e1/(2n1) n 1 e2/3 1 2 .


Show that



1 − 1 2n n ≥ 1 2 .


Hint: For n ≥ 2,



1 − 1 2n n ≥ 1 1+1/(2n − 1)n ≥ 1 e1/(2n−1) n ≥ 1 e2/3 ≥ 1 2 .



May 23, 2022
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