Home
Class 12
MATHS
2*^nC0+2^2*(.^nC1)/2+2^3*(.^nC2)/3+...+2...

`2*^nC_0+2^2*(.^nC_1)/2+2^3*(.^nC_2)/3+...+2^(n+1)*(.^nC_n)/(n+1)=`

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MTG-WBJEE|Exercise WE JEE PREVIOUS YEARS QUESTIONS (CATEGORY 3 : ONE OR MORE THAN ONE OPTION CORRECT TYPE)|5 Videos

  • DEFINITE INTEGRALS

    MTG-WBJEE|Exercise WB JEE WORKOUT (CATEGORY 3 : ONE OR MORE THAN ONE OPTION CORRECT TYPE)|16 Videos

  • CONIC SECTIONS

    MTG-WBJEE|Exercise WB JEE PREVIOUS YEARS QUESTIONS (CATEGORY 3 : One or More than One Option Correct Type)|6 Videos

  • DERIVATIVES

    MTG-WBJEE|Exercise WB JEE PREVIOUS YEARS QUESTIONS|22 Videos

Similar Questions

Explore conceptually related problems

If (nC_0)/(2^n)+2.(nC_1)/2^n+3.(nC_2)/2^n+....(n+1)(nC_n)/2^n=16 then the value of 'n' is

Prove that ""^nC_0+2*""^nC_1+3*""^nC_2+...+(n+1)""^nC_n=(n+2)2^(n-1)

Prove that (""^nC_1)/(""^nC_0)+2*(""^nC_2)/(""^nC_1)+3*(""^nC_3)/(""^nC_2)+...+n*(""^nC_n)/(""^nC_(n-1))=frac{n(n+1)}{2}

nC_(0)-(1)/(2)(^(^^)nC_(1))+(1)/(3)(^(^^)nC_(2))-....+(- 1)^(n)(nC_(n))/(n+1)=

If s_n=""^nC_0+2*""^nC_1+3*""^nC_2+...+(n+1)*""^nC_n then find sum_(n=1)^oos_n .

(nC_(0))^(2)-(nC_(1))^(2)+(nC_(2))^(2)+....+(-1)^(n)(nC_(n))^(2)

If S_n=^nC_0.^nC_1+^nC_1.^nC_2+.....+^nC_(n-1).^nC_n and if S_(n+1)/S_n=15/4 , then the sum of all possible values of n is (A) 2 (B) 4 (C) 6 (D) 8

Prove that ""^nC_0+3*""^nC_1+5*""^nC_2+...+(2n+1)""^nC_n=(n+1)2^(n)

Show that : ""^nC_0*m-""^nC_1*(m-1)+""^nC_2*(m-2)-...+(-1)^n*""^nC_n*(m-n)=0

4^(n)C_(0)+4^(2)(nC_(1))/(3)+4^(3)(nC_(2))/(3)+4^(4)(nC_(3))/(4)+....+4^(n+1)(nC_(n))/(n+1) is equal to

MTG-WBJEE-DEFINITE INTEGRALS-WE JEE PREVIOUS YEARS QUESTIONS (CATEGORY 2 : SINGLE OPTION CORRECT TYPE)
  1. The value of the integral int(1)^(2)e^(x)(log(e)x+(x+1)/(x))dx is

    Text Solution

    |

  2. The value of lim(x->0) ( int0 ^ (x^2) cost^2 dt)/( xsin x) is

    Text Solution

    |

  3. 2*^nC0+2^2*(.^nC1)/2+2^3*(.^nC2)/3+...+2^(n+1)*(.^nCn)/(n+1)=

    Text Solution

    |

  4. If f(x)={{:(2x^(2)+1",",xle1),(4x^(3)-1",",xgt1):}, then int(0)^(2)f(x...

    Text Solution

    |

  5. If I=int(0)^(2)e^(x^(4))(x-alpha)dx=0, then alpha lies in the interval

    Text Solution

    |

  6. The value of lim(xrarr2)int(2)^(x)(3t^(2))/(x-2)dt is

    Text Solution

    |

  7. Let f(x) denote the fractional part of a real number x. Then the value...

    Text Solution

    |

  8. Let f: RvecR be a continuous function which satisfies f(x)= int0^xf(t...

    Text Solution

    |

  9. lim(nrarroo)(sqrt1+sqrt2+…+sqrt(n-1))/(nsqrtn)=

    Text Solution

    |

  10. int0^1log(1/x-1)dx is equal to

    Text Solution

    |

  11. Estimate the absolute value of the integral int(10)^(19)(sinx)/(1+x^8)...

    Text Solution

    |

  12. L e tI1=int0^n[x]dxandI2=int0^n{x}dx ,where [x] and {x} are integral a...

    Text Solution

    |

  13. The value of the integral overset(1)underset(0)int e^(x^(2))dx lies in...

    Text Solution

    |

  14. int0^1000 e^(x-[x])dx

    Text Solution

    |

  15. If M=int(0)^((pi)/2)(cosx)/(x+2)dx and N=int(0)^((pi)/4)(sinxcosx)/((x...

    Text Solution

    |

  16. The value of the integral I = int(1//2014)^(2014)(tan^(-1) x)/x dx is

    Text Solution

    |

  17. Let I=int(pi//4)^(pi//3)(sinx)/(x)dx. Then

    Text Solution

    |

  18. The value of I=int(pi//2)^(5pi//2)(e^(tan^(-1)(sinx)))/(e^(tan^(-1)(si...

    Text Solution

    |

  19. The value of lim(nrarroo)(1)/(n)[sec^(2)""(pi)/(4n)+sec^(2)""(2pi)/(4n...

    Text Solution

    |

  20. The value of the integratio int(-pi//4)^(pi//4)(lambda|sinx|+(mu sinx)...

    Text Solution

    |