बायाँ पक्ष ` = C _ 0 ^ 2 + 3 * C _ 1^ 2 + 5 C _ 2 ^ 2 + ... + ( 2 n + 1 ) C _ n ^ 2 `
= `C _ 0 ^ 2 + ( 1 + 2 ) C_ 1^ 2 + ( 1 + 4 ) C _ 2 ^ 2 + ... + ( 1 + 2n ) C _ n^ 2 `
` = ( C _ 0 ^ 2 + C _ 1 ^ 2 + C_ 2 ^ 2 + ... + C_ n ^ 2 ) + 2 ( C _ 1 ^ 2 + 2 C _ 2 ^ 2 + 3 C _ 3 ^ 2 + ... + n* C _ n^ 2 ) `
` = ""^ ( 2n )C _ n + 2 (n * ""^ ( 2n - 1 ) C _ ( n - 1 ) ) = ( 2n ! ) /( n ! ( 2n - n ) ! ) + 2n * ( ( 2n - 1 ) ! ) /( (n - 1 ) ![ 2n - 1 - (n- 1 ) ] ! ) `
` = ( 2n ! ) /( n! * n! ) + (2n ( 2n - 1 ) ! ) /( ( n - 1 ) ! n! ) = (2n ! ) /( (n! ) ^ 2 ) + ( 2n ! ) /( (n - 1 ) ! n! ) `
` = ( 2n ! ) /( (n! ) ^ 2 ) + ( 2n ! ) /( ( n - 1 ) !n! ) = ( 2n ! ) /( (n! ) ^ 2 ) + ( n* 2 n !) / ( n ( n - 1 ) ! * n ! ) `
` = ( 2n! ) /( ( n! ) ^ 2 ) + ( n * 2n ! ) /( n! * n! ) = (2n ! ) / ( ( n !) ^ 2 ) + ( n * 2n ! ) /( (n! ) ^ 2 ) = ( 2n ! ) /( (n ! ) ^ 2 ) ( 1 + n ) `
` = ( ( n + 1 ) 2n ! ) /( ( n! ) ^ 2 ) = ` दायाँ पक्ष
