Question

1.b is defined by bn = n(−1)n, n ≥ 1

(a) Find Σ when 4 is on top, i=1 at the bottom and b_i at the right hand side

(b) Is b increasing, decreasing, non-increasing or non-decreasing?

Answer 1

(a)

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

$$=1(-1)^1+2(-1)^2+3(-1)^3+4(-1)^4$$

$$=-1+2-3+4=2$$

(b)

$$b_{2k-1}=(-1)^{2k-1}(2k-1)=-(2k-1)<0, k\geq1$$

$$b_{2k}=(-1)^{2k}(2k)=2k>0, k\geq1$$

The sequence $\{b_n\}$ is alternating.

The alternating sequence $\{b_n\}$ is neither increasing nor decreasing .