Home
Class 12
MATHS
lim(nto oo) (1-1/(2^(2)))(1-1/(3^(2)))(1...

`lim_(nto oo) (1-1/(2^(2)))(1-1/(3^(2)))(1-1/(4^(2)))…………….(1-1/(n^(2)))` equals:

A

`3/8`

B

`1/2`

C

`1/4`

D

`1/8`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Prove the following by using the principle of mathematical induction for all n in N (1-(1)/(2^2)) (1-(1)/(3^2))(1-(1)/(4^2))…….(1-(1)/(n^2)) = (n+1)/(2n) " " n >= 2

Definite integration as the limit of a sum : lim_(ntooo)[(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))(1+(3^(2))/(n^(2)))......(1+(n^(2))/(n^(2)))]^(1/n)=.......

Using mathematical induction , show that (1-(1)/(2^2))(1-(2)/(3^2))(1-(1)/(4^2)).....(1-(1)/((n+1)^2))=(n+2)/(2(n+1)), forall n in N .

Definite integration as the limit of a sum : lim_(ntooo)[(1)/(n^(2))sec^(2)""(1)/(n^(2))+(2)/(n^(2))sec^(2)""(4)/(n^(2))+.......+(1)/(n)sec^(2)1] a. 'tan1 b. 1/2tan1 c. 1/2sec1 d. 1/2cosec 1

(1)/(1*2)+(1)/(2*3)+(1)/(3*4)+"…."+(1)/(n(n+1)) equals

lim_(ntooo)(1^(2)+2^(2)+3^(2)+.....+n^(2))/(n^(3)) =........

Definite integration as the limit of a sum : lim_(ntooo)[(1)/(n)+(1)/(sqrt(n^(2)+n))+(1)/(sqrt(n^(2)+2n))+.......+(1)/(sqrt(n^(2)+(n-1)n))]=.........

Definite integration as the limit of a sum : lim_(ntooo)[(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+.........+(1)/(8n)]=........

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

Find the sum: (1)/(3) + (2)/(3^(2)) + (1)/(3^(3)) + (2)/(3^(4)) + (1)/(3^(5)) + (2)/(3^(6)) + …..oo

ALLEN -TEST PAPERS-MATHEMATICS
  1. The value of lim(xto0^(+))(x^(x)+(tanx)^(cosecx)+(cosecx)^(tanx)) is...

    Text Solution

    |

  2. f:RtoR is defined as f(x)=x^(3)+2x^(2)+7x+cos(pix) and g be the invers...

    Text Solution

    |

  3. y=sinx+e^(x) then (d^(2)x)/(dy^(2)) is:

    Text Solution

    |

  4. Let f(x) be a cubic polynomical such that f'(x)=0 at x=1 and x=3, f(1)...

    Text Solution

    |

  5. lim(xto oo)(ln(x^(2)+5x)-2ln(cx+1)=-2 then

    Text Solution

    |

  6. The variable x satisfying the equation |sinxcosx|+sqrt(2+tan^2+cot^2x)...

    Text Solution

    |

  7. If quadratic equation (1+m)x^(2)-2(1+3m)x-2(1+m)=0 has one root greate...

    Text Solution

    |

  8. The quadratic polynomial p(x) has the following properties: p(x)geq0 f...

    Text Solution

    |

  9. Number of points on [0,2] where f(x)={(x{x}+1,(0lexlt1),(2-{x},1lex...

    Text Solution

    |

  10. Let sin theta-cos theta=1 then the value of sin^(3) theta-cos^(3)theta...

    Text Solution

    |

  11. Domain off(x)=log(x^2+5x+6)/([x]-1)where [.] denotes greatest integer ...

    Text Solution

    |

  12. Let f:RtoR f(x)=x+3x^(3)+5x^(5)+………..+1001x^(1001) then which of fol...

    Text Solution

    |

  13. The sum sum(n=1)^oo tan^(-1)(3/(n^2+n-1)) is equal to

    Text Solution

    |

  14. Let f(x)={(cos[x],xge0),(|x|+a,xlt0):} (where [.] denotes greatest i...

    Text Solution

    |

  15. lim(nto oo) (1-1/(2^(2)))(1-1/(3^(2)))(1-1/(4^(2)))…………….(1-1/(n^(2)))...

    Text Solution

    |

  16. The velue of lim(x->0)(sin(3sqrtx)ln(1+3x))/((tan^(- 1)sqrt(x))^2(e^(...

    Text Solution

    |

  17. Let f:RtoR is given by f(x)={(p+qx+x^(2),xlt2),(2px+3qx^(2),xge2):} t...

    Text Solution

    |

  18. Let h (x) = min (x, x^2), x in R, then h (x) is

    Text Solution

    |

  19. Let f(x) be defined as f(x)={([x],-2lexle(-1)/2),(2x^(2)-1,(-1)/2lt...

    Text Solution

    |

  20. Number of points where the function f(x)={(1+["cos"(pix)/2],1ltxle2)...

    Text Solution

    |