Home
Class 11
MATHS
Let Tr denote the rth term of a G.P. for...

Let `T_r` denote the rth term of a G.P. for `r=1,2,3,` If for some positive integers ` ma n d n ,` we have `T_m=1//n^2` and `T_n=1//m^2` , then find the value of `T_(m+n//2.)`

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos
  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

Let T_r be the rth term of an A.P., for r=1,2,3,..... If for some positive integers m ,n , we have T_m=1/na n dT_n=1/m ,t h e nT_(m n) equals a. 1/(m n) b. 1/m+1/n c. 1 d. 0

If "^(2n+1)P_(n-1):^(2n-1)P_n=3:5, then find the value of n .

Let S_n denote the sum upto n terms of an AP . If S_n=n^2P and S_m=m^2P where m,n,p are positive integers and m ne n , then find S_p .

If sum_(r=1)^n T_r=(3^n-1), then find the sum of sum_(r=1)^n1/(T_r) .

If .^(n+r+1)P_(2)=72and.^(n-r)P_(2)=12 then find the values of n and r.

Let T_(n) denote the number of triangles which can be formed using the vertices of a regular polygon of n sides . If T_(n+1)-T_(n)=21 then find the values of n .

Let T_(r) be the rth term of an A.P. If m. T_(m) = n.T_(n) , the show that, T_(m+n) = 0 .

Let t_(r) be the rth term of an A.P. If t_(2), t_(8) and t_(32) are in G.P., then find the common ratio of the G.P.

The mth terms of a G.P is n and its nth term is m. Find its (2m - n)th term.

For a positive integer n let a(n)=1+1/2+1/3+1/4+….+1/ ((2^n)-1) Then

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If S=1/(1xx3xx5)+1/(3xx5xx7)+1/(5xx7xx9)+ddot to infinity, then find t...

    Text Solution

    |

  2. If the sum of the roots of the quadratic equation a x^2+b x+c=0 is equ...

    Text Solution

    |

  3. Let Tr denote the rth term of a G.P. for r=1,2,3, If for some positive...

    Text Solution

    |

  4. Prove that (b^2+c^2)/(b+c)+(c^2+a^2)/(c+a)+(a^2+b^2)/(a+b)> a+b+c

    Text Solution

    |

  5. If y z+z x+x y=12 , and x , y , z are positive values, find the great...

    Text Solution

    |

  6. If S=a1+a2+......+an,ai in R^+ for i=1 to n, then prove that S/(S-a1)...

    Text Solution

    |

  7. If m >1,n in N show that 1^m+2^m+2^(2m)+2^(3m)+...+2^(n m-m)> n^(1-m)...

    Text Solution

    |

  8. If a ,b >0 such that a^3+b^3=2, then show that a+blt=2.

    Text Solution

    |

  9. Prove that 2^n >1+nsqrt(2^(n-1)),AAn >2 where n is a positive integer.

    Text Solution

    |

  10. In a triangle A B C prove that a/(a+c)+b/(c+a)+c/(a+b)<2

    Text Solution

    |

  11. Find the least value of secA+secB+secC in an acute angled triangle.

    Text Solution

    |

  12. Prove that [(n+1)//2]^n >(n !)dot

    Text Solution

    |

  13. If a1+a2+a3+......+an=1 AA ai > 0, i=1,2,3,......,n, then find the ma...

    Text Solution

    |

  14. If a ,b ,c are positive, then prove that a//(b+c)+b//(c+a)+c//(a+b)geq...

    Text Solution

    |

  15. If (log)(10)(x^3+y^3)-(log)(10)(x^2+y^2-x y)lt=2, and x ,y are positiv...

    Text Solution

    |

  16. If log2(a+b)+log2(c+d)ge4 . Then the minimum value of the expression a...

    Text Solution

    |

  17. If a+b+c=1, then prove that 8/(27a b c)>{1/a-1}{1/b-1}{1/c-1}> 8.

    Text Solution

    |

  18. If a ,b , a n dc are distinct positive real numbers such that a+b+c=1,...

    Text Solution

    |

  19. If a^2+b^2+c^2-ab-bc-ca=0 then, prove that a=b=c

    Text Solution

    |

  20. Find the minimum value of 4sin^(2)x+4cos^(2)x .

    Text Solution

    |