Change the bounds of a summation formula I'm currently reading my notes and this appeared and I tried making the left side change into the right side but it's not working. I know you're supposed to use a change in lower bound and use the summation identity but I still can't get n(n-1)/2 appear. Isn't the identity of summation j = n(n+1)/2?
Please check your result once again.

$$\begin{align}3 \sum_{j=2}^n j - (n-1) &amp; = 3 \left(\sum_{j=1}^n j - 1\right) - n + 1 \\ &amp; = \frac{3n(n+1)}{2} - 3 - n + 1 \\ &amp; = \frac{3n(n+1)}{2} - n - 2\end{align}$$
Use something like $$\sum_{j=27}^\infty a_j\;=\;\sum_{j=1}^\infty a_{j+26}$$.