Question:medium

The sum to \(n\) terms of the series \(\sum_{r=1}^n \frac{r}{1+r^2+r^4}\) is

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Use partial fractions: \(\frac{r}{1+r^2+r^4} = \frac{1}{2}\left[\frac{1}{r^2-r+1} - \frac{1}{r^2+r+1}\right]\)
Updated On: Apr 23, 2026
  • \(\frac{n^2+1}{2(n^2+n+1)}\)
  • \(\frac{n^2+n}{2(n^2+n+1)}\)
  • \(\frac{n^2+n}{2(n^2+n+1)}\)
  • \(\frac{n^2+n}{2(n^3+n+1)}\)
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The Correct Option is C

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