Home
Class 11
MATHS
The sum of the series 1+(1/2) ^nC1 +(1/3...

The sum of the series `1+(1/2) ^nC_1 +(1/3) ^nC_2 +....+(1/(n+1)) ^nC_n ` is equal to

A

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

B

`(3 (2^n-1))/(2n)`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    PATHFINDER|Exercise QUESTION BANK |266 Videos
  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

The sum of the series 1+(1)/(2)""^(n)C_(1)+(1)/(3)""^(n)C_(2)+…+(1)/(n+1)""^(n)C_(n) is equal to-

Let S=2/1 ^nC_0+2^2/2 ^nC_1+2^3/3 ^nC_2+....+2^(n+1)/(n+1) ^nC_n . Then S equals

Find the sum of the series 1.n+2(n-1)+3(n-2)+.....n.1 .

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

The sum to n terms of the series 1+2(1+1/n)+3(1+1/n)^2+....... is given by

The sum of the series (1)/(sqrt1+sqrt2)+ (1)/(sqrt2+ sqrt3)+ ...+ (1)/(sqrt(n)+sqrt(n+1)) is equal to-

The value of ,^nC_0 + ^(n+1)C_1 +^(n+2)C_2+……+^(n+k)C_k is equal to

If C_r stands for nC_r , then the sum of the series (2(n/2)!(n/2)!)/(n !)[C_0^2-2C_1^2+3C_2^2-........+(-1)^n(n+1)C_n^2] ,where n is an even positive integer, is

.^18C_15+2(.^18C_16)+^17C_16+1=^nC_3 , then n is equal to

The sum to n terms of the series [1. (1!)+2. (2!)+ 3.(3!)+…] is-

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. The sum of coefficient of integral powers of x in the binomial expansi...

    Text Solution

    |

  2. Number of irrational terms in the binomial expansion of (3^(1//5)+7^(1...

    Text Solution

    |

  3. Coefficient of x^11 in the expansion of (1+x^2)^4(1+x^3)^7(1+x^4)^12 i...

    Text Solution

    |

  4. Let S=2/1^nC0+2^2/2^nC1+2^3/3^nC2+....+2^(n+1)/(n+1)^nCn. Then S equal...

    Text Solution

    |

  5. The coefficient of x^3 in the infinite series expansion of 2/((1-x)(2-...

    Text Solution

    |

  6. The value of sum (nC1)^2+( nC2)^2+(nC3)^2+....+(nCn)^2 is

    Text Solution

    |

  7. If the coefficient of x^8 in (ax^2+1/(bx))^13 is equal to the coeffici...

    Text Solution

    |

  8. The coefficients of three consecutive terms of (1+x)^(n+5) are in the ...

    Text Solution

    |

  9. The coefficient of the term independent of x in the expansion of [((x+...

    Text Solution

    |

  10. Let n be a positive even integer. The ratio of the largest coefficient...

    Text Solution

    |

  11. The sum of the series 1/(1x2)*(25)C0+1/(2x3)*25C1+1/(3x4)*25C2+....+1/...

    Text Solution

    |

  12. If n is a possible integer, then (sqrt3+1)^(2n)-(sqrt3-1)^(2n) is

    Text Solution

    |

  13. Let the coefficients of powers of x in the 2^(nd), 3^(rd) and 4^(th) t...

    Text Solution

    |

  14. The sum of the series 1+(1/2) ^nC1 +(1/3) ^nC2 +....+(1/(n+1)) ^nCn ...

    Text Solution

    |

  15. Let (1+x)^10=sum(r=0)^(10)crx^r and (1+x)^7=sum(r=0)^7drx^r . If P=sum...

    Text Solution

    |

  16. The coefficient of x^10 in the expansion of 1+(1+x)+....+(1+x)^20 is

    Text Solution

    |

  17. The coefficient of x^7 in the expansion of (1-x-x^2+x^3)^6 is

    Text Solution

    |

  18. The number (101)^100-1 is divisible by

    Text Solution

    |

  19. If A and B are coefficients of x^n in the expansions of (1+x)^(2n) and...

    Text Solution

    |

  20. If n gt 1 is an integer and x ne 0, then (1+x)^n-nx-1 is divisible by

    Text Solution

    |