Given \(\sum\limits_{r=2}^{N}{\frac{3r^{2}+3r+1}{r^{3}(r+1)^{3}}}=\frac{1}{8}-\frac{1}{(N+1)^{3

Question

Given $\sum\limits_{r=2}^{N}{\frac{3r^{2}+3r+1}{r^{3}(r+1)^{3}}}=\frac{1}{8}-\frac{1}{(N+1)^{3}}$, deduce an expression for $\sum\limits_{r=2}^{N}{\frac{3r^{2}-3r+1}{3(r-1)^{3}r^{3}}}$.

Accepted Answer

$\frac{1}{3}-\frac{1}{3N^3}$

Sigma Notation By Substitution Q3

Sigma Notation By Substitution Q3

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