Home
Class 12
MATHS
If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2...

If `sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4^2))++sqrt(1+1/((1999)^2)+1/(2000)^2)+=1/x ,`Find x

Text Solution

Verified by Experts

The correct Answer is:
`x = 2000 - (1)/( 2000)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE & SERIES

    RESONANCE ENGLISH|Exercise EXERCISE -1 PART -II RMO|1 Videos

  • SEQUENCE & SERIES

    RESONANCE ENGLISH|Exercise EXERCISE -2 (PART -I PREVIOUS ASKED QUESTION FOR PRE RMO)|15 Videos

  • SEQUENCE & SERIES

    RESONANCE ENGLISH|Exercise SELF PRACTICE PROBLEMS |23 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise SSP|55 Videos

  • TEST PAPER

    RESONANCE ENGLISH|Exercise MATHEMATICS|48 Videos

Similar Questions

Explore conceptually related problems

(sqrt(3)-1)+(1)/(2)(sqrt(3)-1)^(2)+(1)/(3)(sqrt(3)-1)^(3)+….oo

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

If sqrt(1-x^2) + sqrt(1-y^2)=a(x-y) , prove that (dy)/(dx)= sqrt((1-y^2)/(1-x^2))

If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y), prove that (dy)/(dx)=sqrt((1-y^2)/(1-x^2))

If sqrt(1-x^2) + sqrt(1-y^2)=a(x-y) , prove that (dy)/(dx)= sqrt((1-y^2)/(1-x^2))

tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))

y=tan^(-1)((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)))

If sqrt(1-x^(2)) + sqrt(1-y^(2))=a(x-y) , then prove that (dy)/(dx) = sqrt((1-y^(2))/(1-x^(2)))

If sqrt(1-x^(2)) + sqrt(1-y^(2))=a(x-y) , then prove that (dy)/(dx) = sqrt((1-y^(2))/(1-x^(2)))

If sqrt(1-x^(2)) + sqrt(1-y^(2))=a(x-y) , then prove that (dy)/(dx) = sqrt((1-y^(2))/(1-x^(2)))

RESONANCE ENGLISH-SEQUENCE & SERIES -EXERCISE -1 PART -I RMO
  1. The sum of three numbers in A.P. is 27, and their product is 504, find...

    Text Solution

    |

  2. Three friends whose ages form a G.P. divide a certain sum of money in ...

    Text Solution

    |

  3. The roots of the equation x ^(5) - 40 x ^(4) + ax ^(3) + bx ^(2) + cx ...

    Text Solution

    |

  4. Let T(n) denotes the n ^(th) term of a G.P. with common ratio 2 and (l...

    Text Solution

    |

  5. If a, b, c are in A.P. and if (b-c)x^(2)++(c-a)x+a-b=0and2(c+a)x^(2)+(...

    Text Solution

    |

  6. Along a road lies an odd number of stones placed at intervals of 10 m....

    Text Solution

    |

  7. a,b,c are positive real numbers forming a. G.P. If ax ^(2) + 2 bx + c=...

    Text Solution

    |

  8. Determine all pairs (a,b) of real numbers such that 10, a,b,ab are in ...

    Text Solution

    |

  9. If sqrt(1+1/(1^2)+1/(2^2))+sqrt(1+1/(2^2)+1/(3^2))+sqrt(1+1/(3^2)+1/(4...

    Text Solution

    |

  10. If n is any positive integer, then find the number whose square is und...

    Text Solution

    |

  11. Find the sum of infinite terms of the series : (3)/(2.4) + (5)/(1.4.6)...

    Text Solution

    |

  12. If S (1), S (2) , S (3)……., S (2n) are the sums of infinite geometric ...

    Text Solution

    |

  13. Find the nth terms and the sum to n term of the series : 1^(2)+(1^(2...

    Text Solution

    |

  14. Let a (j) = (7)/(4) ((2)/(3)) ^( j -1), j in N. lf b (j) = a (j) ^(2...

    Text Solution

    |

  15. The sequence 9, 18, 27, 36, 45, 54,….. consists of successive mutiple ...

    Text Solution

    |

  16. As show in the figure , the five circles are tangent to one another co...

    Text Solution

    |

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

    Text Solution

    |

  18. Let a sequence whose n^(th) term is {a(n)} be defined as a(1) = 1/2 ...

    Text Solution

    |

  19. If x = (1 ^(2))/(1) =+ (2 ^(2))/( 3) + (3 ^(2))/( 5) +.....+ (1001 ^(2...

    Text Solution

    |

  20. Let K is a positive Integer such that 36 +K , 300 + K , 596 + K are th...

    Text Solution

    |