Progressions

Calculus Level 3

Sn=r=1n2r+1r4+2r3+r2 S_{n}=\sum_{r=1}^n\frac{2r+1}{r^{4}+2r^{3}+r^{2}}

For SnS_n as defined above, S20=mm+1S_{20} = \dfrac{m}{m+1}. Find m+1\sqrt{m+1}.

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