Home
Class 11
MATHS
sum(k=1)^(2n+1) (-1)^(k-1) k^2 =...

`sum_(k=1)^(2n+1) (-1)^(k-1) k^2 =`

A

`(n+1)(2n+1)`

B

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

C

`(n-1) (2n-1)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)|55 Videos

  • LOCUS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|37 Videos

  • MATRICES

    AAKASH SERIES|Exercise LINEAR EQUATIONS - PRACTICE EXERCISE|15 Videos

Similar Questions

Explore conceptually related problems

Use mathematical induction to prove that statement sum_(k = 1)^(n) (2 K - 1)^(2) = (n (2 n - 1) (2n + 1))/( 3) for all n in N

Statement - 1 : The sum of the series 1+ ( 1+2+4) + ( 4+6+9) + ( 9+ 12+ 16) + ... + ( 361 + 380 + 400) is 8000 Statement-2: sum_(k=1)^(n) [ k^(3) - (k-1)^(3) ] = n^(3) , for any natural number 'n'

Given that 0 lt x lt (pi)/(4), (pi)/(4) lt y lt (pi)/(2) and sum_(k = 0)^(infty) (-1)^(k) tan^(2k) x = p, sum_(k = 0)^(infty)(-1)^(k) cot^(2k) y = q then sum_(k = 0)^(infty) tan^(2k) x cot^(2k) y is

If sum_(r = 0)^(2n) a_(r ) (x-2)^(r ) = sum_(r = 0)^(2n) b_(r ) (x-3)^(r ) and a_(k ) =1 for all k ge n then show that b_(n ) =""^((2n+1)) C_((n+1)) .

sum_(i=1)^(n) sum_(j=1)^(i) sum_(k=1)^(j) 1, is equal to

Prove the following sum_(i=1)^(n) sum_(j=1)^(n) sum_(k=1)^(n) sum_(l=1)^(n) (1)=n^(4)

If |a| lt 1, b = sum_(k=1)^(oo) (a^(k))/(k) rArr a=

AAKASH SERIES-MATHEMATICAL INDUCTION-PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)
  1. 2.4 + 4.7 + 6.10+ …. upto (n-1) terms=

    Text Solution

    |

  2. sum(n=0)^( oo) (-1)^(n) x^( n+1)=

    Text Solution

    |

  3. sum(k=1)^(2n+1) (-1)^(k-1) k^2 =

    Text Solution

    |

  4. cos theta + cos 2 theta + cos 3 theta + …. + cos { (n-1) theta}+ cos n...

    Text Solution

    |

  5. If P (n) = 1+2+3+ …. + n is a perfect square N^(2) and N is less than...

    Text Solution

    |

  6. 1 + (x)/( a1) + ( x( x+a1) )/( a1 a2 ) + .... + ( x ( x+a1) (x+ a2)......

    Text Solution

    |

  7. (1)/(2) tan"" ((x)/(2) ) + (1)/( 4) (tan"" (x)/(4) ) + ...... + (1)/(2...

    Text Solution

    |

  8. For any integer n ge 1, then sum(k=1)^(n) k ( k+2) is equal to

    Text Solution

    |

  9. S(n) = 1^(3) + 2^(3) + 3^(3) + …... + n^(3) and T(n) = 1+ 2 + 3+ 4….....

    Text Solution

    |

  10. A = sum of first 10 natural numbers, B = sum of squares of first 10 ...

    Text Solution

    |

  11. If sum (r=1)^(n) t(r) = (1)/( 12) n (n+1) (n+2) then sum(r=1)^(n) (1)...

    Text Solution

    |

  12. 1+ (1+3) + (1+3+ 5) + ….n brackets =

    Text Solution

    |

  13. 1+ ((1)/(3) + (1)/(3^2) ) + (( 1)/( 3^3) + (1)/( 3^4) + (1)/( 3^5) ) ...

    Text Solution

    |

  14. Sum of n^( th) bracket of (1) + (2+ 3+4) + ( 5+ 6+ 7+ 8+9) + ….. is

    Text Solution

    |

  15. { n (n+1) (2n+1) : n in Z} sub

    Text Solution

    |

  16. If a,b and n are natural numbers then a^(2n-1) + b^(2n-1) is divisible...

    Text Solution

    |

  17. If 'a' and 'b'are natural numbers such that a^(2) - b^(2) is prime num...

    Text Solution

    |

  18. AA n in N, 49^(n) + 16n -1 is divisible by

    Text Solution

    |

  19. AA n in , 7^(2n) + 3^(n-1) . 2^(3n-3) is divisible by

    Text Solution

    |

  20. Sum of the cubes of three successive natural number is divisible by

    Text Solution

    |