Question

4. v defined by vn = n! + 2, n ≥ 1.

(a) Find v3

(b) Find  Σ 4 on top , i=1 at the bottom and V_i on the right hand side of Sigma

(c) Is v increasing, decreasing, non-increasing or non-decreasing?

Answer 1

(a)

$$v_3=3!+2=8$$

(b)

$$\displaystyle\sum_{i=1}^{4}v_i=v_1+v_2+v_3+v_4$$

$$=1!+2+2!+2+3!+2+4!+2=41$$

(c)

$$v_{n+1}=(n+1)!+2>n!+2=v_n, n\geq 1$$

The sequence $\{v_n\}$ is (strictly) increasing.