Home
Class 12
MATHS
For any odd integer n ge1, n^(3) - ( n -...

For any odd integer `n ge1`, `n^(3) - ( n - 1)^(3) + "….." + ( -1)^(n-1)1^(3)` equals `:`

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise LATEST QUESTIONS|11 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise Recent competitive Questions|5 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise Recent competitive Questions|5 Videos

  • RELATIONS

    MODERN PUBLICATION|Exercise RCQS|6 Videos

  • SETS

    MODERN PUBLICATION|Exercise Recent Competitive Questions (RCQs)|6 Videos

Similar Questions

Explore conceptually related problems

If n is an odd integer greater than or equal to 1, then the value of : n^(3) - ( n - 1)^(3) + ( n -2)^(3) - "........." + ( - 1)^(n-1) . 1^(3) is :

The sum of : (x+ 2)^(n-1) + ( x+2) ^(n-2) (x+1) + ( x+2)^(n-3) (x+1)^(2) + "......." + ( x+ 1)^(n-1) equals :

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

If A = [(1,1),(1,1)] and n in N , then A^(n) equals :

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

if .^(2n+1)P_(n-1):^(2n-1)P_(n)=7:10 , then .^(n)P_(3) equals

For any integer n, the argument of ((sqrt(3)+i)^(4 n+1))/((1-i sqrt(3))^(4 n)) is

If n is an odd integer, then (1+i)^(6 n)+(1-i)^(6 n) is equal to

If n is a +ve integer, 4^(n)-3 n-1 is divisible by

Let n ( gt 1 ) be a positive integer, the largest integer m such that ( n ^(m) + 1) divides : ( 1+ n + n^(2) + "………" n^(127)) is :

MODERN PUBLICATION-SEQUENCES AND SERIES -MCQ ( Level-II)
  1. Let a^(n) be the nth term of the G.P. of positive numbers. Let sum(n=1...

    Text Solution

    |

  2. Let f(x) be a function satisfying f(x+y) = f(x) f(y) for all x,y in N ...

    Text Solution

    |

  3. For any odd integer n ge1, n^(3) - ( n - 1)^(3) + "….." + ( -1)^(n-1)1...

    Text Solution

    |

  4. The sum to infinity of the series : 1+2 ( 1-(1)/( n )) + 3( 1 - ( 1)...

    Text Solution

    |

  5. If a,b,c are digits, then the rational number represented by 0.c ab ab...

    Text Solution

    |

  6. If I(n) = int(0)^(n) ( 1- sin 2nx)/( 1-cos 2n)dx then I(1) , I(2) , I(...

    Text Solution

    |

  7. If p,q,r , three positive real numbers are in A.P., then the roots of ...

    Text Solution

    |

  8. If a(1),a(2) , a(3),"……..",a(n) are in H.P. , then : (a(1))/( a(2) ...

    Text Solution

    |

  9. The value of sum(r=1)^(n) log ((a^(r ))/( b^(r-1))) is :

    Text Solution

    |

  10. If a(1) , a(2),"………",a(n) are n non-zero real numbers such that ( a(1)...

    Text Solution

    |

  11. The sum of n terms of the series : (1)/( 1.2.3.4) + ( 1)/( 2.3.4.5) ...

    Text Solution

    |

  12. If sum(r=1)^(prop) t(r ) = ( n (n +1) ( n + 2) ( n + 3))/( 8 ) , wher...

    Text Solution

    |

  13. sum(i=1)^(n) sum(j=1)^(i)sum(k=1)^(j) 1 equals :

    Text Solution

    |

  14. If log(x)a,a^(x//2) and log(b)x are in G.P., then x equals :

    Text Solution

    |

  15. If x,y,z are in A.P. and tan^(-1)x , tan^(-1)y and tan^(-1) z are als...

    Text Solution

    |

  16. If P,Q,R be the A.M., G.M., H.M. respectively between any two rational...

    Text Solution

    |

  17. Let S = ( 8 ) /( 5) + ( 16)/( 65) +"...." + ( 128)/( 2^(18) + 1) , th...

    Text Solution

    |

  18. The sides a,b,c of Delta ABC are in G.P. , where log a - log 2b, log ...

    Text Solution

    |

  19. Let alpha, beta be the roots of x^(2) -x + p = 0 and gamma , delta b...

    Text Solution

    |

  20. If the sum of the first 2n terms of the A.P. 2,5,8,"……….." is equal to...

    Text Solution

    |