Find the sum of the following series :-

\((^{ }{ C }_{ 0 }-{ 2 }^{ 2 }\times ^{ }{ C }_{ 1 }+{ 3 }^{ 2 }\times ^{ }{ C }_{ 2 }-.......+{ (-1 })^{ n }({ n+1 })^{ 2 }\times ^{ }{ C }_{ n })\)where n>2.

\(Details\quad and\quad Assumptions\)

\(^{ }{ C }_{ r }=^{ n }{ C }_{ r }\)

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