What’s this sum $\sum\limits_{j=i+1}^n c$ equal to? I thought it was $(n-(i+1))c$ but I’m not sure wouldnt it be $(n-(i+1) +1)c = (n-i-1+1)c = (n-i)c$ ?
2026-04-01 18:37:23.1775068643
What’s this sum equal to?
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Hint: Factoring out a factor of $c$, you get
$$c\sum_{j=i+1}^n 1,$$
so it's $c$ times the number of integers $j$ so that $i+1\leq j\leq n$. How many such integers are there? Try labeling them $1,\cdots,k$ for some $k$ and see what $k$ is.