Wednesday, 3 May 2017

Why are these summations not equivalent?

Hello i have this sum:




$\sum_{j=0}^{n-2}(n-j)$



i try solve of this mode:



$\sum_{j=0}^{n-2}n - \sum_{j=0}^{n-2}j$ or $\sum_{j=0}^{n-2}n + \sum_{j=0}^{n-2}-j$



but in wolfram alpha it not same, and the expected result is n²



This sum is obtained from the following recurrence:




$f(n)= 1 if n<= 1\\
f(n)= n+f(n-1) n>1$



but it not same

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