Sequence of real numbers | Proof of convergence

http://sites.google.com/site/asdfasdf23135/ra12.JPG

Assuming the truth of part a, I proved part b.

But now I am struggling with proving parts a & c.

Part a seems true intuitively. The sqaure root of a number between 0 and 1 is will be larger than that number, and if we take more and more square roots, it will get close to 1, and then if we add two numbers that are close to 1, it must be ≥1.

But how can we write a FORMAL proof of it? How can we construct N and demonstrate exactly that there exists an N such that n≥N => a_n ≥1?

Can someone help me, please?

Any help is much appreciated!

[note: also under discussion in Math Links forum]