Home
Class 12
MATHS
The sum to (n+1) terms of the series C0...

The sum to `(n+1)` terms of the series `C_0/2-C_1/3+C_2/4-C_3/5+......=`

A

`(1)/(n+1)`

B

`(1)/(n+2)`

C

`(1)/(n(n+1))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise NUMERICAL VALUE TYPE FOR JEE MAIN|14 Videos
  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise JEE Archive|56 Videos
  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise LEVEL 1|89 Videos
  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

Similar Questions

Explore conceptually related problems

If C_r stands for nC_r, then the sum of first (n+1) terms of the series a C_0-(a+d)C_1+(a+2d)C_2-(a+3d)C_3+......, is

The sum of the series ""^20 C_0-""^20 C_1+""^20C_2-""^20C_3+...-...+""^20C_10 is:

Sum of n terms of the series 1/(1.2.3.4.)+1/(2.3.4.5) +1/(3.4.5.6)+....

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

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + …+ C_(n) x^(n) , find the sum of the series (C_(0))/(2) -(C_(1))/(6) + (C_(2))/(10) + (C_(3))/(14) -...+ (-1)^(n) (C_(n))/(4n+2) .

The sum of the series ""^20C_0 - ""^20C_1 + ""^20C_2 - ""^20C_3 +…….""^20C_10 is

The sum of the series .^(20)C_(0)-.^(20)C_(1)+ .^(20)C_(2)-.^(20)C_(3)+...-.+ .^(20)C_(10) is -

If C_(0), C_(1) C_(2) ….., denote the binomial coefficients in the expansion of (1 + x)^(n) , then (C_(0))/(2) - (C_(1))/(3) + (C_(2))/(4)- (C_(3))/(5)+...+ (-1)^(n)(C_(n))/(n+2) =

If (1+x)^n=C_0+C_1x+C_2x^2+……..+C_nx^n in N prove that (a) 3 C_0- 8C_1+13C_2-18C_3+...."upto" (n+1) term=0 if n ge 2 (b ) 2C_0+2^2(C_1)/(2)+2^3(C_2)/(3)+2^4C_(3)/4+....+2^(n+1)(C_n)/(n+1)=(3^n+1-1)/(n+1) ( c) C_0^2+(C_1^2)/2+C_2^2/3+....+C_n^2/(n+1)=((2n+1)!)/(((n+1)!)^2)

Find the sum C_0+3C_1+3^2C_2++3^n C_ndot

VMC MODULES ENGLISH-BINOMIAL THEOREM-LEVEL 2
  1. The sum of the series underset(r=1)overset(n)sum(-1)^(r-1)..^(n)C(r)(a...

    Text Solution

    |

  2. Find the sum 2C0+(2^3)/2C1+(2^3)/3C2+(2^4)/4C3++(2^(11))/(11)C(10)dot

    Text Solution

    |

  3. The sum to (n+1) terms of the series C0/2-C1/3+C2/4-C3/5+......=

    Text Solution

    |

  4. If (1+x)^(n)=C(0)+C(1)x+…..+C(n)x^(n), then (C(1))/(C(0))+(2C(2))/(C(1...

    Text Solution

    |

  5. sum(r=0)^(n)(""^(n)C(r))/(r+2) is equal to :

    Text Solution

    |

  6. If .^(47)C(4)+underset(r=1)overset(5)(sum).^(52-r)C(3) is equal to

    Text Solution

    |

  7. sum(r=0)^m .^(n+r)Cn is equal to

    Text Solution

    |

  8. Evaluate sum(i=0)^(n)sum(j=0)^(n) ""^(n)C(j) *""^(j)C(i), ile j .

    Text Solution

    |

  9. sum(r=0)^(n)((r+2)/(r+1))*""^(n)C(r) is equal to :

    Text Solution

    |

  10. The expression (""^(10)C(0))^(2)-(""^(10)C(1))^(2)+(""^(10)C(2))^(2)...

    Text Solution

    |

  11. If C(0),C(1), C(2),...,C(n) denote the cefficients in the expansion...

    Text Solution

    |

  12. If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) +…+ C(n) x^(n) , find the...

    Text Solution

    |

  13. If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) +…+ C(n) x^(n) , find the...

    Text Solution

    |

  14. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+….+C(n)x^(n), then the value of sums...

    Text Solution

    |

  15. If (1+x)^(n)=C(0)+C(1)x+C(2)x^(2)+….+C(n)x^(n), then the value of sums...

    Text Solution

    |

  16. Find the value of underset(0leiltjlen)(sumsum)(.^(n)C(i)+.^(n)C(j)).

    Text Solution

    |

  17. If n is a positive integer and C(k)=""^(n)C(k), then the value of sum(...

    Text Solution

    |

  18. If C(0),C(1),C(2),…,C(n) are the binomial coefficients in the expansio...

    Text Solution

    |

  19. Find the sum of 1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+ ...,

    Text Solution

    |

  20. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+….+a(2n)x^(2n) where a(0), a(...

    Text Solution

    |