Home
Class 12
MATHS
Given x in (-1,0)uu(0,1)and f(x)= sum(n=...

Given `x in (-1,0)uu(0,1)and f(x)= sum_(n=0)^(oo) x^(n)(-1)^(n(n+1)/(2)).` The function `f (x)` is equivalent to a rational function (a)`(1-x)/(1+x^(2))` (b) `(1+x)/(1+x^(2))` (c) `(1)/(1-x)` (d) `(1)/(1+x)`

A

`(1-x)/(1+x^(2))`

B

`(1+x)/(1+x^(2))`

C

`(1)/(1-x)`

D

`(1)/(1+x)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos

  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos

Similar Questions

Explore conceptually related problems

The function y= f(x) = lim_(n to oo) (x^(2n)-1)/(x^(2n)+1) . Is this function same as the function g(x) = "sgn"(|x|)-1) .

If f(x) = sum_(k=2)^(n) (x-(1)/(k-1))(x-(1)/(k)) , then the product of root of f(x) = 0 as n rarr oo , is

If f(x)=lim_(n->oo)[2x+4x^3+6x^5++2n x^(2n-1)] (0ltxlt1) then int f(x)dx is equal to:

Let f(x)=lim_(nto oo) 1/n((x+1/n)^(2)+(x+2/n)^(2)+……….+(x+(n-1)/n)^(2)) Then the minimum value of f(x) is

The function f(x)=cot^(-1)x+x increases in the interval (a) (1,\ oo) (b) (-1,\ oo) (c) (-oo,\ oo) (d) (0,\ oo)

Discuss the continuity of f(x)=(lim)_(n->oo)(x^(2n)-1)/(x^(2n)+1)

Differentiate the following function with respect to x : cos^(-1)((1-x^(2n))/(1+x^(2n))) , 0ltxltoo

The domain of the following function is f(x)=(log)_2(-(log)_(1/2)(1+1/((x^(1/4)))-1) (0,1) (b) (0,1) (1,oo) (d) (1,oo)

lim_(xto0^(-)) (sum_(r=1)^(2n+1)[x^(r)]+(n+1))/(1+[x]+|x|+2x), where ninN and [.] denotes the greatest integer function, equals

If x_1, x_2, x_3,...... x _(2n) are in A.P , then sum _(r=1)^(2n) (-1)^(r+1) x_r^2 is equal to (a) (n)/((2n-1))(x _(1)^(2) -x _(2n) ^(2)) (b) (2n)/((2n-1))(x _(1)^(2) -x _(2n) ^(2)) (c) (n)/((n-1))(x _(1)^(2) -x _(2n) ^(2)) (d) (n)/((2n+1))(x _(1)^(2) -x _(2n) ^(2))

RESONANCE ENGLISH-DPP-QUESTION
  1. Sum of an infinite G.P. is 5/4 times the sum of all the odd terms. The...

    Text Solution

    |

  2. Sum of an infinitely manu terms of a G.P. is 3 times the sum of even t...

    Text Solution

    |

  3. Given x in (-1,0)uu(0,1)and f(x)= sum(n=0)^(oo) x^(n)(-1)^(n(n+1)/(2))...

    Text Solution

    |

  4. Find the value of cos""(pi)/(12)(sin""(5pi)/(12)+cos""(pi)/(4))+sin"...

    Text Solution

    |

  5. If A and B are two sets, then Ann(bar(AuuB)) is equal to :

    Text Solution

    |

  6. A survey shows that 63% of the people watch a news channel whereas ...

    Text Solution

    |

  7. If cos(alpha+beta)=0 then sin(alpha+2beta)=

    Text Solution

    |

  8. Two infinite sets have m and n elements. The number of subsets of t...

    Text Solution

    |

  9. In a certain town, 25% families own a phone and 15% own a car, 65% fam...

    Text Solution

    |

  10. If Xuu{1,2}={1,2,3,5,9}, then :

    Text Solution

    |

  11. If sqrt((1-sinA)/(1+sinA))+(sinA)/(cosA)=(1)/(cosA), for all permissib...

    Text Solution

    |

  12. Let ax^(2)+a^(2)x+2=0 be a quadratic equation, a in R and S be the set...

    Text Solution

    |

  13. Let ax^(2)+a^(2)x+2=0 be a quadratic equation, a in R and S be the set...

    Text Solution

    |

  14. The arithmaeic mean of the nine numbers in the given set {9,99,999,….....

    Text Solution

    |

  15. If a, b and c are in AP and if the equations (b-c)x^2 + (c -a)x+(a-b)=...

    Text Solution

    |

  16. Solve :(tanx-(1)/(sqrt3))(cosx-(1)/(2))le0.

    Text Solution

    |

  17. The value of {:(cos5^(@)cos20^(@)+cos35^(@)cos50^(@)),(-sin5^(@)sin20^...

    Text Solution

    |

  18. The value of "cosec"10^(@)+"cosec"50^(@)-"cosec"70^(@) is

    Text Solution

    |

  19. Suppose alpha,beta,gammaa n ddelta are the interior angles of regular ...

    Text Solution

    |

  20. If y=1costheta+2cos2theta+3cos3theta++99 cos 99theta , the maximum val...

    Text Solution

    |