# Progressions

**Calculus**Level 3

\[ S_{n}=\sum_{r=1}^n\frac{2r+1}{r^{4}+2r^{3}+r^{2}}\]

For \(S_n\) as defined above, \(S_{20} = \dfrac{m}{m+1}\). Find \(\sqrt{m+1}\).

\[ S_{n}=\sum_{r=1}^n\frac{2r+1}{r^{4}+2r^{3}+r^{2}}\]

For \(S_n\) as defined above, \(S_{20} = \dfrac{m}{m+1}\). Find \(\sqrt{m+1}\).

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