Question 73
Let $(a_n)_{n \ge 1}$ be the sequence given by $a_1 = 2$ and $a_{n+1} = 1 + \frac{1}{a_1 a_2 \dots a_n}$, $\forall n \ge 1$.
a) Find the general term of the sequence.
b) Put $S = \sum_{k=1}^{n} \frac{2}{(k^3 + k^2)a_{2k+1}}$ in a close form and show that $S \lt 1$.
a) Find the general term of the sequence.
b) Put $S = \sum_{k=1}^{n} \frac{2}{(k^3 + k^2)a_{2k+1}}$ in a close form and show that $S \lt 1$.