Home
Class 12
MATHS
If Sigma(r=1)^(50) (r^2)/(r^2+(11-r)^2),...

If `Sigma_(r=1)^(50) (r^2)/(r^2+(11-r)^2)`, then the value of n is __________

Text Solution

Verified by Experts

The correct Answer is:
50
`S=1/(2^(0)+2^(50))+1/(2^(1)+2^(50))+..+1/(2^(100)+2^(50))`
`S=1/(2^(100)+2^(50))+1/(2^(99)+2^(50))+…+1/(2^(0)+2^(50))`
`2S=1/(2^(50)+1/(2^(50))+..` 100 times
`thereforeS=50/(2^(50))`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise JEE Main Previous Year|12 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise JEE Advanced Previous Year|16 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise EXERCIESE ( MATRIX MATCH TYPE )|3 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

If ^n P_r=^n P_(r+1)a n d^n C_r=^n C_(r-1,) then the value of n+r is.

Find the sum Sigma_(r=1)^(oo) (r)/(r^4+1/4)

Let lt a_n gt be an arithmetic sequence of 99 terms such that sum of its odd numbered terms is 1000 then the value of Sigma_(r=1)^(50) (-1)^((r(r+1))/2).a_(2r-1) is _________.

Find the sum Sigma_(r=1)^(oo)(3n^2+1)/((n^2-1)^3)

If sum_(r=1)^(r=n)(r^(4)+r^(2)+1)/(r^(4)+r)=(675)/(26) , then n equal to

Find the sum Sigma_(r=1)^(oo) (r-2)/((r+2)(r+3)(r+4))

If the sum of the series Sigma_(n=0)^(oo) r^(n),|r|le 1 is s, then find the sum of the series Sigma_(n=0)^(oo) r^(2n),|r|le 1

Find the sum Sigma_(r=1)^(n) r/((r+1)!) . Also, find the sum of infinite terms.

Let P = sum_(r=1)^(50) (""^(50+r)C_(r)(2r-1))/(""^(50)C_(r)(50+r)), Q = sum__(r=1)^(50) (""^(50)C_(r))^(2), R = sum_(r=0)^(100) (-1)^(r) (""^(100)C_(r))^(2) The value of P - Q is equal to

CENGAGE-PROGRESSION AND SERIES-Exercise (Numerical)
  1. Let an= 16,4,1,… be a geometric sequence .Define Pn as the product of ...

    Text Solution

    |

  2. The terms a1, a2, a3 from an arithmetic sequence whose sum s 18. The t...

    Text Solution

    |

  3. Let the sum of first three terms of G.P. with real terms be 13/12 and ...

    Text Solution

    |

  4. The first term of an arithmetic progression is 1 and the sum of the fi...

    Text Solution

    |

  5. The digits in units's place of number (10^(2013)-1)/(10^33-1) is..

    Text Solution

    |

  6. The number of positive integral ordered pairs of (a ,b) such that 6,a ...

    Text Solution

    |

  7. If the roots of 10 x^3-n x^2-54 x-27=0 are in harmonic oprogresi...

    Text Solution

    |

  8. Given a,b,c are in A.P.,b,c,d are in G.P and c,d,e are in H.P .If a=2 ...

    Text Solution

    |

  9. Let Sk be sum of an indinite G.P whose first term is 'K' and commmon r...

    Text Solution

    |

  10. The value of the sum Sigma(i=1)^(20) i(1/i+1/(i+1)+1/(i+2)+.....+1/(20...

    Text Solution

    |

  11. The difference between the sum of the first k terms of the series 1^3+...

    Text Solution

    |

  12. The value of the Sigma(n=0)^(oo) (2n+3)/(3^n) is equal to .

    Text Solution

    |

  13. The sum of the infinite Arithmetico -Geometric progression3,4,4,… is .

    Text Solution

    |

  14. Sigma(r=1)^(50)(r^2)/(r^2+(11-r)^2) is equal to .

    Text Solution

    |

  15. If Sigma(r=1)^(50) (r^2)/(r^2+(11-r)^2), then the value of n is

    Text Solution

    |

  16. Let lt an gt be an arithmetic sequence of 99 terms such that sum of it...

    Text Solution

    |

  17. Find the sum of series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1))^2...

    Text Solution

    |

  18. Let S=Sigma(n=1)^(999) (1)/((sqrt(n)+sqrt(n+1))(4sqrt(n)+4sqrtn+1)) , ...

    Text Solution

    |

  19. Let S denote sum of the series 3/(2^3)+4/(2^4 .3)+5/(2^6 .3)+6/(2^7 .5...

    Text Solution

    |

  20. The sum (7)/(2^2xx5^2)+13/(5^2xx8^2)+19/(8^2xx11^2)+…10 terms is S, th...

    Text Solution

    |