Let n be positive integer such that (1+ x) n = C 0 +C 1 x+ C 2 x 2 +……..C n x n then –
(i) The value of 
, is-
Text Solution
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Ans.
(i)
Sol. 
= (C 0 ± C 1 ) 2 + (C 0 ± C 2 ) 2 +….+ (C 0 ± C n )2 + (C 1 ± C 2 ) 2 +….+ (C 1 ± C n ) 2 +…+ (C 2 ± C n ) 2 … …. …. …. …. …. ….
…. …. … …. …. …. ….
…. …. …. …. ….
+(C n–2 ± C n–1 )
2 + (C n–2 ± C n ) 2 + (C n–1 ± C n ) 2 = n(C 0
2 + C 1 2 …..+C 2 2 ) + 2 
= n. 2n C n + [2 2n – 2n C n ]
= (n 
1). 2n C n ±2 2n
(ii)
Sol. 
. s C r
= 
( s C 0 + s C 1 +…..+ s C s ) = 
= 
= (1+2) n –1 = 3 n –1
(iii)
Sol. 
= 
+ 
. 
= n. 2 n–1 . 2 n + 2 n . n2 n–1 = n.2 2n
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