Binomial TheoremHard
Question
The sum 
(r + 1) Cr2 is equal to :
(r + 1) Cr2 is equal to :Options
A.
B.
C.
D.
Solution
∵ (1 + x)n = C0 + C1x +.......+ Cnxn
Multiply by x & then differentiate
(1 + x)n + x. n(1 + x)n-1 = C0 + 2C1x +.........+ (n + 1)Cnxn ..........(i)
and (x + 1)n = C0xn + C1xn-1 +.......+ Cn .......(ii)
Multiply (i) & (ii) & equate the coefficient of xn on
both side
C02 + 2C12 + ........+ (n + 1) Cn2 = 2nCn + n. 2n-1Cn-1 =
= (n + 2)
Multiply by x & then differentiate
(1 + x)n + x. n(1 + x)n-1 = C0 + 2C1x +.........+ (n + 1)Cnxn ..........(i)
and (x + 1)n = C0xn + C1xn-1 +.......+ Cn .......(ii)
Multiply (i) & (ii) & equate the coefficient of xn on
both side
C02 + 2C12 + ........+ (n + 1) Cn2 = 2nCn + n. 2n-1Cn-1 =
= (n + 2)Create a free account to view solution
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