Does n n matter?

Algebra Level 4

Find the value of :

{ ( C 0 + C 3 + . . . ) − 1 2 ( C 1 + C 2 + C 4 + C 5 + . . . . ) } 2 + 3 4 { C 1 − C 2 + C 4 − C 5 . . . . . } 2 { \{ { (C }_{ 0 }+{ C }_{ 3 }+...)-\frac { 1 }{ 2 } ({ C }_{ 1 }+{ C }_{ 2 }+{ C }_{ 4 }+{ C }_{ 5 }+....)\} }^{ 2 }+\\ \frac { 3 }{ 4 } { \{ { C }_{ 1 }-{ C }_{ 2 }+{ C }_{ 4 }-{ C }_{ 5 }.....\} }^{ 2 }

C r r e p r e s e n t s n ! r ! ( n − r ) ! { C }_{ r }\quad represents\quad \frac { n! }{ r!(n-r)! }

And if you feel that the answer must depend on n n , give 1729 1729 as your answer!

T h i s p r o b l e m i s n o t o r i g i n a l This\quad problem\quad is\quad not\quad original


The answer is 1.

A Former Brilliant Member by A Former Brilliant Member

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