$$\sum\limits_{1 \le k \le n} {O(n)} $$ where O(n) stands for order n is:

Express T(n) in terms of the harmonic number H_n = $$\sum\limits_{t = 1}^n {1/i,n \ge 1} $$ where T(n) satisfies the recurrence relation, T(n) = $${{n + 1} \over 2}$$ T(n-1) + 1, for $$n \ge 2$$ and T(1) = 1 What is the the asymptotic behavior of T(n) as a function of n?

What is the generating function G (z) for the sequence of Fibonacci numbers?

Solve the recurrence equations
T (n) = T (n - 1) + n
T (1) = 1