Home
Class 12
MATHS
(1)/(n !)+(1)/(2 !(n-2) !)+(1)/(4 !(n-4)...

`(1)/(n !)+(1)/(2 !(n-2) !)+(1)/(4 !(n-4) !)+.... `=

A

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

B

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

C

3) `(2^(n))/(n !) `

D

4) `(2^(n-2))/((n-1) !) `

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DIFFERENTIATION

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|221 Videos

  • CIRCLES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|272 Videos

Similar Questions

Explore conceptually related problems

For a positive integer n, let a_(n) = 1+( 1)/( 2) +( 1)/( 3) + ( 1)/( 4) + "......." + ( 1)/(( 2^(n) - 1)) . Then :

{:(" Lt"),(n rarr oo):} ( 1/n + (1)/(sqrt(n^(2)-1))+(1)/(sqrt(n^(2)-4))+..."to n terms")=

Prove that by using the principle of mathematical induction for all n in N : (1)/(2)+ (1)/(4)+ (1)/(8)+ ......+ (1)/(2^(n))= 1-(1)/(2^(n))

Prove that by using the principle of mathematical induction for all n in N : (1)/(1.2.3)+ (1)/(2.3.4)+ (1)/(3.4.5)+....+ (1)/(n(n+1)(n+2))= (n(n+3))/(4(n+1)(n+2))

lim_(n rarr oo) ((1)/(1.2) + (1)/(2.3) + (1)/(3.4) +…..+ (1)/(n(n+1))) is :

Prove that by using the principle of mathematical induction for all n in N : 1+ (1)/((1+2))+ (1)/((1+2+3))+ .....+(1)/((1+2+3+n))= (2n)/(n+1)

If S denotes the sum to infinity and S_(n) , the sum of n terms of the series 1+( 1)/(2) +( 1)/( 4) + ( 1)/( 8 ) +"………….", such that S-S_(n) lt ( 1)/( 1000) , then the least value of n is :

For all n ge 1 prove that (1)/(1.2)+ (1)/(2.3)+(1)/(3.4)+.....+(1)/(n(n+1))=(n)/(n+1)

Prove that by using the principle of mathematical induction for all n in N : (1)/(2.5)+ (1)/(5.8) + (1)/(8.11)+ ...+(1)/((3n-1)(3n+2))= (n)/(6n+4)

HIMALAYA PUBLICATION-BINOMIAL THEOREM-QUESTION BANK
  1. If the second term in the expansion ((a)^(1/13)+(a)/(sqrt(a^(-1))))^...

    Text Solution

    |

  2. The sum of last ten coefficients in the expansion of (1+x)^(19) whe...

    Text Solution

    |

  3. (1)/(n !)+(1)/(2 !(n-2) !)+(1)/(4 !(n-4) !)+.... =

    Text Solution

    |

  4. The coefficient of x^(5) in the expansion of (1+x)^(21)+(1+x)^(22)+....

    Text Solution

    |

  5. The coefficient of x^(6) in: [(1+x)^(6)+(1+x)^(7)+ . . .+(1+x)^(15)]...

    Text Solution

    |

  6. Numerically the greatest term in the expansion of (3-5 x)^(15) when ...

    Text Solution

    |

  7. The greatest term in the expansion of (1+x)^(10) when x=(2)/(3) is

    Text Solution

    |

  8. The coefficients of (2 r+4)^(th) and (r-2)^(th) terms in the expansion...

    Text Solution

    |

  9. If the coefficients of r^(th) , (r+1)^(t h) and (r+2)^(th ) terms in...

    Text Solution

    |

  10. The number of terms in the expansion of (2 x+3 y-4 z)^(n) is

    Text Solution

    |

  11. If (1 +x + x^(2))^(n) = a(0) + a(1) x + a(2) x^(2) + … + a(2n) x^(2n) ...

    Text Solution

    |

  12. If (1+x+x^(2))^(n) = a(0)+a(1) x+a(2) x^(2)+.. .+a(2 n) x^(2 n) then ...

    Text Solution

    |

  13. If (1 +x + x^(2))^(n) = a(0) + a(1) x + a(2) x^(2) + … + a(2n) x^(2n) ...

    Text Solution

    |

  14. The value of sum(r=1)^(10)r(n C(r))/(n C(r-1)) =

    Text Solution

    |

  15. 6^(n)-5 n when divided by 25 leaves the remainder

    Text Solution

    |

  16. 2^(60) when divided by 7 leaves the remainder

    Text Solution

    |

  17. If the middle term of ((1)/(x)+xsinx)^(10) is equal to 7(7)/(8) then v...

    Text Solution

    |

  18. If A and B are coefficients of x^(n) in the expansion of (1+x)^(2n) an...

    Text Solution

    |

  19. If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x...

    Text Solution

    |

  20. The coefficients of x^(n) in the expansion of (1+x)^(2n) and (1+x)^(2n...

    Text Solution

    |