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Sum of the series 2C0+C1/2 2^2 +C2/3 2...

Sum of the series
`2C_0+C_1/2 2^2 +C_2/3 2^3+………+C_n/(n+1) 2^(n+1)`

A

`(3^(n+1)-1) /(n-1)`

B

`(3^(n+1)-1) /(n+1)`

C

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

D

`(3^(n-1)-1) /(n+1)`

Text Solution

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The correct Answer is:
B
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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. The coefficients of x^p and x^q in the expansion of (1+x)^(p+q) are

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  2. If x^m occurs in the expansion of (x+(1/x^2))^(2n) then the coefficien...

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  3. Sum of the series 2C0+C1/2 2^2 +C2/3 2^3+………+Cn/(n+1) 2^(n+1)

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  4. The value of nC0. ^nCn +^nC1 . ^nC(n-1)++……..+^nCn . ^nC0

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  5. If (1+x)^(15)=C0+C1x+C2x^2+……..+C(15)x^(15) then ,^15C0^2-^15C1^2+^15C...

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  6. If sn= sum(r=0)^n 1/(^"nCr) and tn=sum(r=0)^n r/("^nCr) then tn/sn is ...

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  7. The fractional part of =(2^(4n))/15 is

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  8. If the fourth term in the expansion of (px+(1/x))^n is independent of ...

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  9. Find the coefficient of x^20 in the expression of (1+x^2)^40(x^2+2+1/x...

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  10. Let n be a positive integer such that (1+x+x^2)^n=a0+a1x+a2x^2+…….+a(2...

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  11. Let n be a positive integer such that (1+x+x^2)^n=a0+a1x+a2x^2+…….+a(2...

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  12. The greatest integer which divides the number 101^(100)-1 is

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  13. Coefficient of x^(11) in the expansion of (1+3x+2x^2)^6 is equal to

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  14. Show that 101^(50)gt 99^(50)+100^(50)

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  15. The greatest term (numerically) in the expansion of (2+3x)^9 when x=3/...

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  16. If agt0 and coefficients of x^5 and x^(15) in the expansion of (x^2+a/...

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  17. 1/(n!)+1/(2!(n-2)!)+1/(4!(n-4)!)+ …… is equal to

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  18. The coefficients of x^n in (1+x/(1!)+x^2/(2!)+……+x^n/(n!))^2 is

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  19. The sum of the coefficients of all the integral powers of x in the exp...

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  20. The coefficient of x^m in (1+x)^r+ (1+x)^(r+1)+(1+x)^(r+2)+………+(1+x)^n...

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