Question
Thu May 10, 2012 By: Student Learner

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Expert Reply
Fri May 11, 2012
(1+x)n=Co+C1x+C2x2+....Cnxn
 
So, from the above binomial expansion, we can write
Co=n!/n!
C1=n!/(n-1)!
C2=n!/(n-2)!2!
.............
.............
Cn=n!/(n)!
From the above values of coefficients, we can calculate the followings:
C1/C= n
2C2/C= 2xn!(n-1)!/(n-2)!2!n! = n-1
3C3/C= 3xn!(n-2)!2!/(n-3)!3!n!= n-2
..............
..............
nCn/Cn-1 = n/n = 1
 
So, the required sum becomes,
C1/C+ 2C2/C+ 3C3/C.....+nCn/Cn-1 
= n+ n-1 + n-2 + n-3....... + 1
= 1+2+3+.......+n
= n(n+1)/2
 
Hence, (C) is the correct option.
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