ISI PREVIOUS YEAR QUESTION SOLUTION (B.MATH/B.STAT). SEQUENCE, SERIES QUESTION.

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ISI PREVIOUS YEAR QUESTION SOLUTION (B.MATH/B.STAT). SEQUENCE, SERIES QUESTION. Let {u_n }_(n greater than 1) be a sequence of real numbers defined as u_1=1 and u_(n+1)=u_n+1/u_n all n greater than 1, Prove that
u_n less than (3sqrt n)/2 all n.