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Find the coefficient of x^(r) in the fol...

Find the coefficient of `x^(r)` in the following expression :
`(x+n)^(n)+(x+2)^(n-1)(x+1)+(x+2)^(n-2)(x+1)^(2)+.....+(x+1)^(n)`

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Verified by Experts

The correct Answer is:
`((n+1)!)/(r!(n+1-r)!).\(2^(n+1-r)-1)`
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CHHAYA PUBLICATION-BINOMIAL THEOREM -EXERCISE ( Long answer Type Questions )
  1. If the coefficients of the consicutive four terms in the expansion of ...

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  2. If n be a positive integer and if the 3rd , 4th , 5th and 6th terms in...

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  3. Find the coefficient of x^(r) in the following expression : (x+n)^(...

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  4. If the first three terms in the expansion of (1+x)^(n) are in A .P . ,...

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  5. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : C(1)...

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  6. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : C(1)...

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  7. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : (C(0...

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  8. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : (C(0...

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  9. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : C(0)...

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  10. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : C(0)...

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  11. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : (C(1...

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  12. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : (C(0...

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  13. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : (C(1)...

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  14. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : C(0)...

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  15. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : C(0)...

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  16. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show :

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  17. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show :

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  18. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show :

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  19. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+.....+C(n)x^(n) then show : 3.^(...

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  20. The power of a of 10thterm in the extension (a+2b)^20-

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