convergence at a specific value

Question

I have a series $S_n=\sum_{i=1}^{n} a*(1-i)$ where $a$ is an unknown constant independent of $i$. Is there a way to figure out for which $n$ the above expression converges to the value 0.01?

After some calculations I derived $S_n=a*n-a*n*(n+1)/2$

If I take the lim to infinity I only find out whether the series converges or diverges.

Thank you for your time.

Answer 1

From your computation it is easy to see that $$ \lim_{n\to\infty}S_n=\begin{cases}0 & \text{if }a=0,\\ -\infty & \text{if }a>0,\\ +\infty & \text{if }a<0.\end{cases} $$