Define the sequence (L_n) by
L_n=1/(n+1)+1/(n+2)+1/(n+3)+ … + 1/2n for n ≥1
Show using an inductive or non-inductive argument that
L_(n +1)=L_n + [1/((2n +1)(2n +2))] for n ≥1
and
L_n<n(1/(n +1)) for n ≥2
Many thanks.
Are you serious? Why would you be given a problem you aren't equipped to solve.
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