Home
Class 12
MATHS
If a1,a2,a3, ,an are an A.P. of non-z...

If `a_1,a_2,a_3, ,a_n` are an A.P. of non-zero terms, prove that `1/(a_1+a_2)+1/(a_1+a_3)++1/(a_(n-1)+a_n)=(n-1)/(a_1+a_n)dot`

A

`(n-1)/(a_(1)a_(n))`

B

`(n)/(a_(1)a_(n))`

C

`(n+1)/(a_(1)a_(n))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 1

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MCQS|50 Videos
  • MOCK TEST 3

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MCQS|50 Videos

Similar Questions

Explore conceptually related problems

If a_1,a_2,a_3,.....,a_n are in AP, prove that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+...+1/(a_(n-1)a_n)=(n-1)/(a_1a_n) .

If the nonzero numbers a_1,a_2,a_3,....,a_n are in AP, prove that 1/(a_1a_2a_3)+1/(a_2a_3a_4)+...+1/(a_(n-2)a_(n-1)a_n)=1/(2(a_2-a_1))(1/(a_1a_2)-1/(a_(n-1)a_n)) .

If 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : (1-a_1)(1-a_2)(1-a_3)...(1-a_(n-1)) =n.

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""

If a_1,a_2,a_3,…………..a_n are in A.P. whose common difference is d, show tht sum_2^ntan^-1 d/(1+a_(n-1)a_n)= tan^-1 ((a_n-a_1)/(1+a_na_n))

If 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : 1+a_1+a_2+…+a_(n-1) =0.

Let a_1,a_2,a_3 …. a_n be in A.P. If 1/(a_1a_n)+1/(a_2a_(n-1)) +… + 1/(a_n a_1) = k/(a_1 + a_n) (1/a_1 + 1/a_2 + …. 1/a_n) , then k is equal to :

If a ,a_1, a_2, a_3, a_(2n),b are in A.P. and a ,g_1,g_2,g_3, ,g_(2n),b . are in G.P. and h s the H.M. of aa n db , then prove that (a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h

If a_i>0, i=1, 2, 3,..., n then prove that a_1/a_2+a_2/a_3+a_3/a_4+...+a_(n-1)/a_n+a_n/a_1gen .

Let r be the common ratio of the GP a_1,a_2,a_3,....,a_n . Show that 1/(a_1^m+a_2^m)+1/(a_2^m+a_3^m)+....+1/(a_(n-1)^m+a_n^m)=(1-r^((1-n)m))/(a_1^m(r^m-r^-m)) .

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MOCK TEST 2-MCQS
  1. The line (x)/(2)=-(y)/(3)=(z)/(1) is vertical. The direction cosines o...

    Text Solution

    |

  2. The perpendicular distance of the origin from the plane which makes in...

    Text Solution

    |

  3. If a1,a2,a3, ,an are an A.P. of non-zero terms, prove that 1/(a1+a2...

    Text Solution

    |

  4. Which of the following to is the common region for x+y le 10, x ge 5, ...

    Text Solution

    |

  5. The function f(x)=(e^(tanx)-1)/(e^(tanx)+1) is discontinuous at x is e...

    Text Solution

    |

  6. Without rotating the original coordinate axes, to which point should o...

    Text Solution

    |

  7. if x^y . y^x =16 then dy/dx at (2,2) is equal to

    Text Solution

    |

  8. A spherical balloon is punped at the rate of 10 "inch"^(3) min^(-1), t...

    Text Solution

    |

  9. int(3+2cosx)/((2+3cosx)^(2))dx is equal to

    Text Solution

    |

  10. If int((sqrt(x))^(5))/((sqrt(x))^(7)+x^(6))dx=lamdaln(1+2cosx)/((2+cos...

    Text Solution

    |

  11. The value of int(0)^(pi//2)(1+2cosx)/((2+cosx)^(2))dx is

    Text Solution

    |

  12. The circumcentre of the triangle formed by the lines, xy + 2x + 2y + 4...

    Text Solution

    |

  13. If sintheta=sinalpha, then

    Text Solution

    |

  14. The sum of of the mean and variance of a binomial distribution is 15 a...

    Text Solution

    |

  15. . Which one of the following is possible (a) sintheta = (a^2 + b^2)/(...

    Text Solution

    |

  16. Let alphaandbeta be such that piltalpha-betalt3pi. If sinalpha+si...

    Text Solution

    |

  17. If A is a square matrix of order 2xx2 such that A^(2)=O then,

    Text Solution

    |

  18. If G is the centroid of a DeltaABC, then GA^(2)+GB^(2)+GC^(2) is equal...

    Text Solution

    |

  19. If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents a pair of pa...

    Text Solution

    |

  20. Differentiate sin^(-1)((2x)/(1+x^2)) with respect to tan^(-1)((2...

    Text Solution

    |