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## Homework Statement

Prove that a

_{n+2}=a

_{n+1}+a

_{n}where a

_{1}=1 and a

_{2}=1 is monotonically increasing.

## Homework Equations

A sequence is monotonically increasing if a

_{n+1}≥a

_{n}for all n[itex]\in[/itex]

**N**.

## The Attempt at a Solution

Base cases:

a

_{1}≤a

_{2}because 1=1.

a

_{2}≤a

_{3}because 1<2.

Am I supposed to prove that a

_{n}≤a

_{n+1}now? I'm not sure how to do that.

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