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I have the below series :

(1 * 0) + (2 * 1) + (3 * 2) + (4 * 3) + ... + (n * (n-1))

Is it possible to have a generalised formula for this. Also such series like the above would be an AP(arithmetic progression) or GP(geometric progression) ?

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  • $\begingroup$ Please edit to include your efforts. Note that there are standard expressions for sums of the form $\sum_{k=1}^n k^p$ for natural numbers $p$. $\endgroup$
    – lulu
    Commented Jan 7, 2022 at 20:21
  • $\begingroup$ Could you please elaborate as I am new to this. Just went through the link you shared and not sure how Faulhaber's formula would be applicable here $\endgroup$
    – DockYard
    Commented Jan 7, 2022 at 20:27
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    $\begingroup$ Your sum is $\sum_{k=1}^n k(k-1)=\sum_{k=1}^{n}(k^2-k)=\sum_{k=1}^{n}k^2-\sum_{k=1}^nk$. $\endgroup$
    – lulu
    Commented Jan 7, 2022 at 20:54

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