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## Homework Statement

Consider the sequence of real numbers x

_{1}, x

_{2}, x

_{3},.... defined by the relations x

_{1}= 1

and x

_{n+1}=[tex]\sqrt{1 + 2x

_{n}}[/tex]

1. Use mathematical induction to show that x

_{n+1}> x

_{n}

for all n [tex]\geq[/tex] 1.

## The Attempt at a Solution

I'm a bit thrown off by this question because it seems very obvious that it would be greater. if x

_{1}=1 is it safe to assume that x

_{n}=n? and if so I feel like this proof is stupid cause it shows right in front of you that its greater. any help is great thanks.