- #1

acynicsmind

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## Homework Statement

Show the sequence {X_n} defined by X_1 = 1, X_n+1 = X_n + 1/X_n for n > 1 obeys the inequality X_n > sqrt(n) for all n >= 2.

## Homework Equations

## The Attempt at a Solution

For n = 2, 2 > sqrt(2) and for n = 3, 2.5 > sqrt(2.5). So it holds so far. What to do here after initial step for the inductive step is confusing me. I've never seen an induction proof with an inequality before today and the ones I've looked at online are not helpful at all.

Any help is appreciated. Thank you.