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 bi at the right hand side (b) Is b increasing, decreasing, non-increasing or non-decreasing?

(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 .