Question
Question: The value of (n + 2).C<sub>0</sub> 2<sup>n+1</sup> – (n + 1). C<sub>1</sub>2<sup>n</sup> + n.C<sub>2...
The value of (n + 2).C0 2n+1 – (n + 1). C12n + n.C2 2n–1 ... is
A
4(1 + n)
B
4n
C
2n
D
2(n + 2)
Answer
4(1 + n)
Explanation
Solution
(x – 1)n = C0 xn – C1 xn–1 + C2xn–2..........
x2(x – 1)n = C0 xn+2 – C1xn+1 + C2xn........
differentiating w.r.t. x
2x(x – 1)n + x2n (x – 1)n–1 = (n + 2) C0xn+1 –
(n + 1) C1xn + nC2xn–1.......
Now use x = 2
Ž 4 + 4n