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

`2.C_0 + (2^2)/(2).C_1 + (2^3)/(3).C_2 + ……+(2^11)/(11).C_10 = `

A

`((3^(11)+1))/(11)`

B

`(3^(11)-1)/(11)`

C

`(3^7 +1)/(7)`

D

`(4^7 -1)/(7)`

Text Solution

Verified by Experts

The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-BINOMIAL THEOREM-EXERCISE 1B (BINOMIAL COEFFICIENTS)
  1. C3//4+C5//6+C7//8+….=

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  2. C0+(C1 x)/(2)+(C2 x^2)/(3)+…...+(Cn x^n)/(n+1)=

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

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  4. k. C0 + k^2 . (C1)/(2)+k^3. (C2)/(3)+…..+ k^(n+1). (Cn)/(n+1)=

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  5. 2. C0+ 2^2 (C1)/(2)+2^3. (C2)/(3)+…....+2^(n+1). (Cn)/(n+1)=

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  6. (C0)/(2)+(C1)/(3)+(C2)/(4)+…...+(Cn)/(n+2)=

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  7. The sum of (n+1) terms of the series (C0)/(2)-(C1)/(3)+(C2)/(4)-(C3)/(...

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  8. (C0)/(2)+(C1)/(6)+(C2)/(12)+…..+ (Cn)/((n+1)(n+2))=

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  9. Show that (2^(2) *C(0) )/(1*2)+(2^(3)*C(1))/(2*3)+(2^(4) *C(2))/(3*4)+...

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  10. C0 C1+C1 C2 + C2 C3+…+ C(n-1) Cn=

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  11. If (C0 + C1) (C1+C2)…(C(n-1) + Cn)=k C0 C1 C2… Cn then k=

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  12. If (1)/(1!(n-1)!) + (1)/(3!(n-3)!) + (1)/(5!(n-5)!) +…. =

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  13. sum(r=0)^(n) (""^n Cr)^2 =

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  14. C0^2+3.C1^2+5. C2^2+….+(2n+1) .Cn^2=

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  15. If Cr denotes the binomial coefficient ""^n Cr then (-1) C0^2 + 2C1^2+...

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  16. If n is odd then C0^2 - C1^2+C2^2-…....+(-1)^n Cn^2=

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  17. If n is even then C0^2 - C1^2+C2^2-…....+(-1)^n Cn^2=

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  18. ""^((2n + 1))C0 - ""^((2n+ 1))C1 + ""^((2n + 1))C2 - ……+""^((2n + 1))C...

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  19. Prove that (""^(2n)C(0))^(2)-(""^(2n)C(1))^(2)+(""^(2n)C(2))-(""^(2n...

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  20. C1//1-C2//2+C3//3-C4//4+…+(-1)^(n-1) Cn//n=

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