Home
Class 12
MATHS
The value of lim(nrarroo)(1^(2)-2^(2)+3^...

The value of `lim_(nrarroo)(1^(2)-2^(2)+3^(2)-4^(2)+5^(2)….+(2n+1)^(2))/(n^(2))` is equal to

A

2

B

4

C

6

D

8

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • NTA JEE MOCK TEST 60

    NTA MOCK TESTS|Exercise MATHEMATICS|25 Videos

  • NTA JEE MOCK TEST 62

    NTA MOCK TESTS|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

The value of lim_(nrarroo)Sigma_(r=1)^(n)((2r)/(n^(2)))e^((r^(2))/(n^(2))) is equal to

lim_(n rarr oo)(1^(2)+2^(2)+3^(2)+.........+n^(2))/(n^(3)) is equal to -

The value of lim_(x rarr oo)(5^(n+1)+3^(n)-2^(2n))/(5^(n)+2^(n)+3^(2n+1))

The value of lim_(xto oo)(1^(3)+2^(3)+3^(3)+……..+n^(3))/((n^(2)+1)^(2))

lim_(n to oo) (1^(2)+2^(2)+3^(2)+…+n^(2))/(n^(3)) is equal to

The value of lim_(n rarr oo)[(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))++(1)/(2n)] is

The value of lim_(nrarroo) ((sqrtn^(2)+n-1)/(n))^(2sqrt(n^(2)+n-1)) is

The value of lim_(nrarroo)([x]+[2^(2)x]+[3^(2)x]+…+[n^(2)x])/(1^(2)+2^(2)+3^(2)+….+n^(2)) is equal to (where [x] represents the greatest integer part of x)

The value of lim_(nrarroo)((1)/(2n)+(1)/(2n+1)+(1)/(2n+2)+…..+(1)/(4n)) is equal to

The value of lim_(nrarroo)(cos.(x)/(2)cos.(x)/(4)cos.(x)/(8)………cos.(x)/(2^(n+1))) is equal to

NTA MOCK TESTS-NTA JEE MOCK TEST 61-MATHEMATICS
  1. Number of roots of the equation 2sqrt(2x+1)=2x-1 is 0 (b) 1 (c) 2 (...

    Text Solution

    |

  2. Let the n^(th) term of a series be given by tn = (n^2 -n-2)/(n^2+3n),n...

    Text Solution

    |

  3. The value of lim(nrarroo)(1^(2)-2^(2)+3^(2)-4^(2)+5^(2)….+(2n+1)^(2))/...

    Text Solution

    |

  4. Two ships are sailling in the sea on the two sides of a lighthouse. If...

    Text Solution

    |

  5. If [sin^(-1)x]^(2)-2[sin^(-1)x]+1le0 (where, [.] represents the greate...

    Text Solution

    |

  6. Let f:R rarr R be a function defined as f(x)=(x^(2)-6)/(x^(2)+2), then...

    Text Solution

    |

  7. If the variate of a distribution takes the values 1^(2), 2^(2), 3^(2),...

    Text Solution

    |

  8. The point of intersection of tangents drawn to the hyperbola (x^2)/(a^...

    Text Solution

    |

  9. The value of the integral int(0)^(pi)(e^(|cosx|)sinx)/(1+e^(cotx))dx i...

    Text Solution

    |

  10. The curve y=f(x) in the first quadrant is such that the y - intercept ...

    Text Solution

    |

  11. The value of the integral I=int(2x^(9)+x^(10))/((x^(2)+x^(3))^(3))dx i...

    Text Solution

    |

  12. If A, B and C are square matrices of same order and I is an identity m...

    Text Solution

    |

  13. The system of equations alpha(x-1)+y+z=-1, x+alpha(y-1)+z=-1 and x+y+a...

    Text Solution

    |

  14. If vectors 4vecp+vecq, 2 vecp-3vecq and 5vecp-3vecq, 5vecp+3vecq are a...

    Text Solution

    |

  15. The equation of the plane through the points (2,-1,0), (3,-4,5) parall...

    Text Solution

    |

  16. The line 2x+3y=12 meets the coordinates axes at A and B respectively. ...

    Text Solution

    |

  17. The extremities of a diagonal of a rectangle which are parallel to the...

    Text Solution

    |

  18. The ordinates of points P and Q on the parabola y^2=12x are in the rat...

    Text Solution

    |

  19. The area (in sq. untis) bounded by [x+y]=2 with the co - ordinate axes...

    Text Solution

    |

  20. Out of 1000 boys in a school, 300 played cricket, 380 played hockey an...

    Text Solution

    |