Undetermined Coefficients (Part 3)

Algebra Level 4

\[\sum _{ n=1 }^{ 50 }{ \left( 2n-1 \right) { \left( n+2 \right) }^{ 2 } } =1\cdot { 3 }^{ 2 }+3\cdot { 4 }^{ 2 }+5\cdot { 5 }^{ 2 }+\cdots +99\cdot { 52 }^{ 2 } = \, ? \]


You may want to read the wiki page: Method of undetermined coefficients.
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