Home
Class 12
MATHS
If Sn=1/(2n)+1/(sqrt(4n^2-1))+1/(sqrt(4n...

If `S_n=1/(2n)+1/(sqrt(4n^2-1))+1/(sqrt(4n^2-4))++1/(sqrt(3n^2+2n-1)),n in N ,` then `("lim")_(nvecoo)S_n` is equal to `pi/2` (b) 2 (c) 1 (d) `pi/6`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

lim_(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)

lim_(n->oo)[1/sqrt(2n-1^2) +1/sqrt(4n-2^2)+1/sqrt(6n-3^2)+...+1/n]

Evaluate: ("lim")_(n rarr oo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(sqrt(3n^2)))

If x_1=sqrt(3) and x_(n+1)=(x_n)/(1+sqrt(1+x_ n^2)),AA n in N then lim_(n->oo)2^n x_n is equal to

IfS_n=[1/(1+sqrt(n))+1/(2+sqrt(2n))++1/(n+sqrt(n^2))],t h e n(lim)_(n rarr oo)S_n is equal to (a)log 2 (b) log4 (c)log 8 (d) none of these

If S_n=[1/(1+sqrt(n))+1/(2+sqrt(2n))+....+1/(n+sqrt(n^2))] then (lim)_(n ->oo)S_n is equal to (A) log 2 (B) log4 (C) log8 (D) none of these

For all n in N, 1 + 1/(sqrt(2))+1/(sqrt(3))+1/(sqrt(4))++1/(sqrt(n))

(lim)_(n->oo)(n !)/((n+1)!+n !) is equal to a. 1 b . 0 c. 2 d. 1/2

If x_1=3 and x_(n+1)=sqrt(2+x_n),ngeq1,t h e n""("lim")_(xrarroo)x_n is (a) -1 (b) 2 (c) sqrt(5) (d) 3

lim_(n to oo)[(sqrt(n+1)+sqrt(n+2)+....+sqrt(2n))/(n sqrt((n)))]

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. The area of the closed figure bounded by x=-1,x=2,a n d y={-x^2+2,xlt...

    Text Solution

    |

  2. Evaluate int(0)^(pi//2)(cosx)/((1+sinx)(2+sinx))dx.

    Text Solution

    |

  3. If Sn=1/(2n)+1/(sqrt(4n^2-1))+1/(sqrt(4n^2-4))++1/(sqrt(3n^2+2n-1)),n ...

    Text Solution

    |

  4. The function f satisfies the functional equation 3f(x)+2f((x+59)/(x1))...

    Text Solution

    |

  5. The reflection of the point vec a in the plane vec rdot vec n=q i...

    Text Solution

    |

  6. Find the equation of tangent to y=int(x^(2))^(x^(3))(dt)/(sqrt(1+t^(2)...

    Text Solution

    |

  7. Let f be differentiable for all x , If f(1)=-2a n df^(prime)(x)geq2 fo...

    Text Solution

    |

  8. If f1(x)=x ,f2(x)=1-x ,f3(x)=1/x ,f4(x)=1/(1-x),f5(x)=x/(x-x),f5(x)=x/...

    Text Solution

    |

  9. Let f(x)a n dg(x) be two continuous functions defined from RvecR , suc...

    Text Solution

    |

  10. If int((x-1)dx)/(x^(2)sqrt(2x^(2)-2x+1))=sqrt(f(x))/(g(x))+C, where f(...

    Text Solution

    |

  11. If vec a , vec b , vec c are unit vector, prove that | vec a- vec b|^...

    Text Solution

    |

  12. Let lambda=int0^1(dx)/(1+x^3),p=(lim)(n->oo)[(prod(r=1)^n(n^3+r^3)...

    Text Solution

    |

  13. For f(x)=sin^2x ,x in (0,pi) point of inflection is: pi/6 (b) (2pi)/4...

    Text Solution

    |

  14. If z and bar z represent adjacent vertices of a regular polygon of n s...

    Text Solution

    |

  15. If z=((1+isqrt(3))^2)/(4i(1-isqrt(3)))i sacom p l e xnu m b e r ,t h e...

    Text Solution

    |

  16. If vec a+2"" vec b+3"" vec c="" vec0 and |"" vec a|=6,|"" vec b|=3a n...

    Text Solution

    |

  17. Function f(x)=sin(lnx)-"cos"(lnx) is (a)M.I. in [e^(2npipi/4),e^(2np...

    Text Solution

    |

  18. tan(sec^(-1) (1/x))=sin(cos^(-1) (1/sqrt(5)))

    Text Solution

    |

  19. Let : f(x)={(sina x^2)/(x^2),x!=0 3/4+1/(4a),x=0 for what values of a...

    Text Solution

    |

  20. The value of sin(pi/3-sin^(-1)(4/5)) is (a) (3sqrt(3)-4)/(10) (b) (3...

    Text Solution

    |