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The coefficint of x^r in f(x)=(x+2)^n+(x+2)^n-1(x+1)+....(x+1)^n is (a)n+1Cr(2^(n+r)-1) (b)n+1Cr(2^(n-r)-1) (c)n+1Cr(2^(n-r+1)-1) (d)none of these

The coefficint of x^r in
f(x)=(x+2)^n+(x+2)^n-1(x+1)+....(x+1)^n is
(a)n+1Cr(2^(n+r)-1)
(b)n+1Cr(2^(n-r)-1)
(c)n+1Cr(2^(n-r+1)-1)
(d)none of these

Grade:12

1 Answers

Pratham Ashish
17 Points
14 years ago

hi vaibhav,

d given exp is a gp wid r = (x+1)/(x+2)

just write d sum of d given gp , u will get

here , a = (x+2)^n

and sum = a(1-r^n)/(1-r)

after simplifying u will get (x+2)( (x+2)^n - (x+1)^n ) )

nw take 2 from (x+2)^n  and write in simple form as 2^n (1+ x/2)^n and u know dat coeff of x^r is nCr ,so use dis n u will get d final result as

(2^(n-r+1) - 1)*((n+1)Cr ) - nCr so ans wud be (d)none of these.

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