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C0 + (C1)/(2) + (C2)/(2^2) + (C3)/(2^3)+...

` C_0 + (C_1)/(2) + (C_2)/(2^2) + (C_3)/(2^3)+…..+(C_n)/(2^n)=`

A

`(1//2)^n`

B

`(3//2)^n`

C

`(3//2)^(2n)`

D

`(3//2)^(-n)`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-BINOMIAL THEOREM-PRACTICE EXERCISE
  1. If n = (sqrt2 +1)^6. Then the integer just greater than n is

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  2. 1.C0 + 3.C1+ 3^2.C2+….+3^n.Cn =

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  3. C0 + (C1)/(2) + (C2)/(2^2) + (C3)/(2^3)+…..+(Cn)/(2^n)=

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  4. ""^11C0 + ""^11C1 + ""^11C2 + ……+ ""^11C5 =

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  5. C0^2 + C1^2 + C2^2 - ………-C15^2 =

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  6. 1/2.""^10C0 -""^10C1 +2.""^10C2 - 2^2.""^10C3+…..+2^9. ""^10C10 =

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  7. ""^(2n +1)C0^2 -""^(2n+1)C1^2 + ""^(2n+1)C2^2 -…….- ""^(2n+1)C(2n+1)^2...

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  8. Prove that following i) 2.C(0)+5.C(1)+8.C(2)+…..+(3n+2)C(n)=(3n+4).2...

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  9. ""^20C0 + ""^20C1 + ""^20C2+…….+""^20C10 =

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

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

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

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  13. 1.""^20C1 - 2.""^20C2 + 3.""^20C3 - …..-20.""^20C20 =

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  14. (1+x+x^2 + ……+x^p)^n = a0 + a1x + a2 x^2 + ….+a(np) x^(np) rArr a1 + 2...

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  15. C1 + 4.C2 +7.C3 +…….+(3n-2).Cn=

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

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

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  18. ""^11C0^2 - ""^11C1^2 + ""^11C2^2 - ""^11C3^2 + ……- "^11C11^2 =

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

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

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