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If sum(r=0)^(n) ((r+2)/(r+1))""^(n)C(r)=...

If `sum_(r=0)^(n) ((r+2)/(r+1))""^(n)C_(r)=(2^(8)-1)/(6)`. then n is

A

8

B

4

C

6

D

5

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(r=0)overset(n)sum((r+1)/(r+1)+(1)/(r+1)).^(n)C_(1)`
`= underset(r=0)overset(n)sum.^(n)C_(r)+underset(r=0)overset(n)sum(.^(n)C_(r))/(r+1)`
`= 2^(n)+(1)/(n+1).underset(r=0)overset(n)sum.^(n+1)C_(r+1)`
`= 2^(n)+(2^(n+1)-1)/(n+1)`
`= ((n+3)2^(n)-1)/(n+1)`
`= (2^(8)-1)/(6)`
`rArr n = 5`
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CENGAGE-BINOMIAL THEOREM-Exercise (Single)
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  3. If sum(r=0)^(n) ((r+2)/(r+1))""^(n)C(r)=(2^(8)-1)/(6). then n is

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  7. If (1+x)^n=C0+C1x+C2x^2++Cn x^n ,t h e nC0C2+C1C3+C2C4++C(n-2)Cn= ((2...

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  8. ^404C4-^303C4.^4C1+^202C4.^4C2-^101C4.^4C3=

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  9. The value of sum(r=0)^(40) r""^(40)C(r)""^(30)C(r) is

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  10. The value of sum(r=1)^(15) (r2^(r))/((r+2)!) is equal to

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  13. If (1+x^(2))^(n) =sum(r=0)^(n) a(r)x^(r )= (1+x+x^(2)+x^(3))^(100). If...

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  15. The value of sum(r=0)^(20) r(20-r)(""^(20)C(r))^(2) is equal to

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  16. If f(x) = .^(40)C(1).x(1-x)^(39) + 2..^(40)C(2)x^(2)(1-x)^(38)+3..^(40...

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  17. If a(n) = sum(r=0)^(n) (1)/(""^(n)C(r)), then the value of (sumsum)(0l...

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  18. In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be 4...

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