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
View Solution FreeMore Binomial Theorem Questions
Let R = (5√5 + 11)31 = I + f, where I is an integer and f is the fractional part of R, then R. f is equal to -...If (15Cr + 15Cr-1) (15C15-r + 15C16-r) = (16C13)2, then the value of r is -...If the (r +1)th term in the expansion of contains a and b to one and the same power, then the value of r is -...Middle term in the expansion of (x2 − 2x)10 will be -...In the expansion of...