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If ar is the coefficient of x^r in the e...

If `a_r` is the coefficient of `x^r` in the expansion of `(1+x)^n` then `a_1/a_0 + 2.a_2/a_1 + 3.a_3/a_2 + …..+n.(a_n)/(a_(n-1))` =

A

`(n(n+1))/(2)`

B

`(n(n+3))/(2)`

C

`(n(n-1))/(2)`

D

`n^2`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-BINOMIAL THEOREM-PRACTICE EXERCISE
  1. ""^20C0 + ""^20C1 + ""^20C2+…….+""^20C10 =

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  2. C1 + 2. C2 + 3. C3 + …... + n. Cn=

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  3. If ar is the coefficient of x^r in the expansion of (1+x)^n then a1/a0...

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  4. If (1+x)^n = C0 + C1 x+ C2 x^2 + ….....+ Cn x^n, then C0+2. C1 +3. C...

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  5. 1.""^20C1 - 2.""^20C2 + 3.""^20C3 - …..-20.""^20C20 =

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  6. (1+x+x^2 + ……+x^p)^n = a0 + a1x + a2 x^2 + ….+a(np) x^(np) rArr a1 + 2...

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  7. C1 + 4.C2 +7.C3 +…….+(3n-2).Cn=

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  8. sum(r=1)^(n) (-1)^(r-1) ""^nCr(a - r) =

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  9. 2.C0 + (2^2)/(2).C1 + (2^3)/(3).C2 + ……+(2^11)/(11).C10 =

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  10. ""^11C0^2 - ""^11C1^2 + ""^11C2^2 - ""^11C3^2 + ……- "^11C11^2 =

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  11. (C0)/(1) + (C2)/(3) + (C4)/(5) + ……+(C16)/(17) =

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  12. (C1)/(2) + (C3)/(4) + …….+(C15)/(16)=

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  13. The coefficient of x^3 in (1-4x)^(1//2) is

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  14. The range of x for which the expansion of (1-3/x)^(-3//4) is valid is

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  15. The range of x of which the expansion of (2-3x^2)^(-11/2)is valid is

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  16. The fifth term of (1 - (2x)/(3))^(3//4) is

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  17. For |x| lt 1, the (r + 1)^(th) term in the expansion of sqrt(1 - x) is

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  18. The general term of (2a - 3b)^(-1//2) is

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  19. In the expansion of (1+x+x^2+x^3+…..oo)^3, coefficient of x^3 is

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  20. In the expansion of (1-2x+3x^2 -4x^3+…."to")^4 coefficient of x^2 is

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