Saturday, 7 March 2015

calculus - How to prove that a sequence is unbounded

I want to ask, how to start a proof that shows a sequence to be unbounded




Define a sequence $\{X_n\}$ by



$$X_1 = 1 ,\quad X_{n+1} = X_n + \sqrt{X_n} \quad \text{for}\ n \geq 1$$



Prove that $\{X_n\}$ is unbounded.

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