Home
Class 12
MATHS
Let a(n)=int(0)^(pi//2)(1-sint )^(n) sin...

Let `a_(n)=int_(0)^(pi//2)(1-sint )^(n) sin 2t,`
then `lim_(n to oo)sum_(n=1)^(n)(a_(n))/(n)`is equal to

A

`1//2`

B

`1`

C

`4//3`

D

`3//2`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 1|15 Videos
  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 2|14 Videos
  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos
  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

a_ (n) = int_ (0) ^ ((pi) / (2)) (1-sin t) ^ (n) sin2tdt ten lim_ (n rarr oo) sum_ (n = 1) ^ (n) (a_ ( n)) / (n) is equal to

Let: a_(n)=int_(0)^((pi)/(2))(1-sin t)^(n)sin2tdt Then find the value of lim_(n rarr oo)na_(n)

lim_(n to oo) " " sum_(r=2n+1)^(3n) (n)/(r^(2)-n^(2)) is equal to

If sum_(r=1)^(n)T_(r)=(n(n+1)(n+2)(n+3))/(12) then 4(lim_(x rarr oo)sum_(x-1)^(n)(1)/(T_(r))) is equal to

Let I_(n)=int_(0)^(pi//2)x^(n)cosxdx, where in is a non-negative integer Then sum_(n=2)^(oo)((I_(n))/(n!)+(I_(n-2))/((n-2)!)) equals-

If sum_(r=1)^(n)a_(r)=(1)/(6)n(n+1)(n+2) for all n>=1 then lim_(n rarr oo)sum_(r=1)^(n)(1)/(a_(r)) is

If A=[a_(ij)]_(n xx n,) where a_(ij)=i^(100)+j^(100) then lim_(n rarr oo)((sum_(i=1)^(n)a_(ij))/(n^(101))) equals

For n in N, let a_(n)=sum_(k=1)^(n)2k and b_(n)=sum_(k=1)^(n)(2k-1)* then lim_(n rarr oo)(sqrt(a)_(n)-sqrt(b_(n))) is equal to

lim_(n to oo) (n^(p) sin^(2)(n!))/(n +1) , 0 lt p lt 1 , is equal to-

If sum_(r=1)^(n) a_(r)=(1)/(6)n(n+1)(m+2) for all nge1 , then lim_(ntooo) sum_(r=1)^(n) (1)/(a_(r)) , is

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let a(n)=int(0)^(pi//2)(1-sint )^(n) sin 2t, then lim(n to oo)sum(n...

    Text Solution

    |

  2. The value of int(-pi//2)^(pi//2) (x^(2)cos x )/(1+e^(x)) dx is equal ...

    Text Solution

    |

  3. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

    Text Solution

    |

  4. Let f(x)=7 tan^(8) x +7 tan^(6) x-3 tan^(4) x-3 tan^(2)x for all x in...

    Text Solution

    |

  5. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

    Text Solution

    |

  6. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  7. Let F:R- R be a thrice differentiable function. Suppose that F(1)=0,F(...

    Text Solution

    |

  8. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  9. Let f: RvecR be a function defined by f(x)={[x],xlt=2 0,x >2 where [...

    Text Solution

    |

  10. If alpha=int0^1(e^9x+3tan^((-1)x))((12+9x^2)/(1+x^2))dxw h e r etan^(-...

    Text Solution

    |

  11. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

    Text Solution

    |

  12. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  13. Match the conditions/ expressions in Column I with statement in Column...

    Text Solution

    |

  14. Match List I with List II and select the correct answer using codes gi...

    Text Solution

    |

  15. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dxi s

    Text Solution

    |

  16. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  17. The value of int(sqrt(ln2))^(sqrt(ln3)) (xsinx^2)/(sinx^2+sin(ln6-x^2)...

    Text Solution

    |

  18. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

    Text Solution

    |

  19. The value of int(0)^(1) (x^(4)(1-x)^(4))/(1+x^(2)) dx is (are)

    Text Solution

    |

  20. For a in R ( the set of all real number) , a ne -1, lim(n to oo)((1^...

    Text Solution

    |

  21. Consider the statements : P : There exists some x IR such that f(x)...

    Text Solution

    |