calculus - I don't know how to solve this math sequence

I'm new here and I need help with these sequences. I'm in my first calculus class and everything up to now is great except for the part with all the sequences and series, especially these two. I tried doing them myself, but I couldn't find the answer. My teacher gave us a document with 20 questions, and I did everything else, but I'm stuck on these questions about the convergence, limits, and sum. Other than that, I can manage to do everything else by myself, so it would be very appreciated if you could help me out.

FYI I translated these math questions from French, so it might not be perfectly translated. Thanks.

Question 1 :

$$a _ { 1 } = 2 , \quad a _ { n + 1 } = \frac { 1 } { 3 - a _ { n } }$$

a) Prove that the sequence is decreasing

b) find $\lim _ { n \rightarrow \infty } a _ { n }$

c) Prove $0 < a _ { n } \leq 2$

d) Does $\sum _ { n = 1 } ^ { \infty } a _ { n + 1 }$ converges?

Thank you.