# Limit calculation

phonic
Dear members,

I am calculating the following limit:

$$\lim_{t\rightarrow \infty} \sum_{k=1}^{t-2} \frac{\lambda^{t-k-1}}{k}$$
where
$$0 < \lambda <1$$

Does anybody know how to do it? Thanks a lot!

$$0\leq \lim_{t\rightarrow \infty} \sum_{k=1}^{t-2} \frac{\lambda^{t-k-1}}{k}=\lim_{t\rightarrow \infty} \lambda^t \sum_{k=1}^{t-2} \frac{\lambda^{k-1}}{k} \leq \lim_{t\rightarrow \infty} \lambda^t \sum_{k=1}^{\infty} \frac{\lambda^{k-1}}{k}$$