# Prove an infinite limit

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1. Homework Statement

Is this proof correct?
Let K>0, and choose N such that N >= K2, then for all n in the naturals, and n>=N, sqrt(n)+7>=sqrt(N)>=K

Is this proof correct?

RPinPA
Homework Helper
Yes, you need to wrap a little formal language around it to make it a formal proof, but that's the argument. You might want to state and prove that ##\sqrt{n}## is monotonically strictly increasing, i.e. ##\sqrt{m} > \sqrt{n} \iff m > n##, unless that's already been established in your course.

So I'd wind up with a closing line, "therefore [state the definition of going to ##\infty## as ##n \rightarrow \infty##]".