/sci/ - Science & Math

>Prove that the sequence 10^-n converges to 0
>Prove that sqrt(1+(sqrt(1+... = golden ratio
>Prove that the bounded sequence [math]x_n[/math] such that [math](2 - x_n)(x_n+1) = 1[/math] converges to 1
>Prove that the sequence a_n = (1/n^2)([x] + [2x] + ... [nx]) converges to x/2

What
the
fuck

I'm going to start a math major in like a week and these are some of the problems the last weeks of intro to calculus. I'm really good at self-studying, I've studied a lot of undergraduate stuff these months and I've managed to master a lot of exercises from books (Spivak, Herstein, Enderton)

But I feel like a fucking brainlet whenever I check sequence related stuff. I can do convergence tests and proofs related to infinite series but I can't prove a fucking sequence convergence. Heck, I'm even able to prove some functions' limits through epsilon-delta

So, any help? What's a good book that'll help me prove sequence theorems/exercises? Rudin is too topologic, Spivak is too simple, Stewart doesn't even feature proofs.

also... am I panicking too soon for not being able to do these problems?