Home
Class 12
MATHS
If a ,a1, a2, a3, a(2n),b are in A.P. a...

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`

A

2nh

B

`n/h`

C

nh

D

`(2n)/h`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    VMC MODULES ENGLISH|Exercise LEVEL-2|34 Videos

  • SEQUENCE AND SERIES

    VMC MODULES ENGLISH|Exercise JEE MAIN & Advance ( ARCHIVE)|46 Videos

  • SEQUENCE AND SERIES

    VMC MODULES ENGLISH|Exercise JEE MAIN & Advance ( ARCHIVE)|46 Videos

  • REVISION TEST-2 JEE

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

  • STRAIGHT LINES

    VMC MODULES ENGLISH|Exercise JEE Advanced Archive (State true or false: Q. 42)|1 Videos

Similar Questions

Explore conceptually related problems

If a_1, a_2,...... ,a_n >0, then prove that (a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)+.....+(a_(n-1))/(a_n)+(a_n)/(a_1)> n

If a_1, a_2, a_3,.....a_n are in H.P. and a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 a_n , then k is equal to

If a_1,a_2,a_3, ,a_n are an A.P. of non-zero terms, prove that 1/(a_1a_2)+1/(a_2a_3)++1/(a_(n-1)a_n)= (n-1)/(a_1a_n)

If a_1,a_2,a_3,...,a_(n+1) are in A.P. , then 1/(a_1a_2)+1/(a_2a_3)....+1/(a_na_(n+1)) is

Let a_1, a_2, a_3, ...a_(n) be an AP. then: 1 / (a_1 a_n) + 1 / (a_2 a_(n-1)) + 1 /(a_3a_(n-2))+......+ 1 /(a_(n) a_1) =

If a_r>0, r in N and a_1.a_2,....a_(2n) are in A.P then (a_1+a_2)/(sqrta_1+sqrta_2)+(a_2+a_(2n-1))/(sqrta_2+sqrta_3)+.....+(a_n+a_(n+1))/(sqrt a_n+sqrta_(n+1))=

If a_1,a_2,a_3,……a_n are in A.P. [1/(a_1a_n)+1/(a_2a_(n-1))+1/(a_3a_(n-2))+..+1/(a_na_1)]

If a_1,a_2,a_3, ,a_n are in A.P., where a_i >0 for all i , show that 1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_2)+sqrt(a_3))+ ..+1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot

If a_1,a_2,a_3, ,a_n are in A.P., where a_i >0 for all i , show that 1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_2)+sqrt(a_3))++1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot

If a_1,a_2,a_3, ,a_n are in A.P., where a_i >0 for all i , show that 1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_1)+sqrt(a_3))++1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot

VMC MODULES ENGLISH-SEQUENCE AND SERIES -LEVEL-1
  1. Let a1,a2,a3 …. an be in A.P. If 1/(a1an)+1/(a2a(n-1))+… + 1/(an a...

    Text Solution

    |

  2. Sum to infinity of the series 2/3 - 5/6 + 2/3 -11/24 +….. Is

    Text Solution

    |

  3. If a ,a1, a2, a3, a(2n),b are in A.P. and a ,g1,g2,g3, ,g(2n),b . are...

    Text Solution

    |

  4. If I(r)=r(r^2-1), then sum(r=2)^n 1/(I(r)) is equal to

    Text Solution

    |

  5. If sum(r=1)^n Tr=n(2n^2+9n+13), then find the sum sum(r=1)^nsqrt(Tr)do...

    Text Solution

    |

  6. Let (1 + x^2)^2 (1 + x)^n = A0 +A1 x+A2 x^2 + ...... If A0, A1, A2, a...

    Text Solution

    |

  7. If 1/1^3 + (1+2)/(1^3+2^3)+(1+2+3)/(1^3+2^3+3^3) +.......n terms then ...

    Text Solution

    |

  8. If x1, x2, x3,...... x (2n) are in A.P, then sum (r=1)^(2n) (-1)^(r...

    Text Solution

    |

  9. If (a2a3)/(a1a4) = (a2+a3)/(a1+a4)=3 ((a2 -a3)/(a1-a4)) then a1,a2, a3...

    Text Solution

    |

  10. In the sequence 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8, . . . . . ., where n co...

    Text Solution

    |

  11. The coefficient of x^15 in the product (1-x)(1-2x) (1-2^2 x) (1-2^3 ...

    Text Solution

    |

  12. Let a1=0 and a1,a2,a3 …. , an be real numbers such that |ai|=|a(i-1) ...

    Text Solution

    |

  13. Find the sum of the products of the ten numbers pm1,pm2,pm3,pm4, and p...

    Text Solution

    |

  14. If 1/1^4+1/2^4+1/3^4+...+oo=pi^4/90, then 1/1^4+1/3^4+1/5^4+...+oo=

    Text Solution

    |

  15. If n is an odd integer greater than or equal to 1, the value of =n^(3)...

    Text Solution

    |

  16. Let S(k) =sum( i =0) ^(oo) (1)/((k +1)^(t)), then sum (k =1) ^(n) kS(...

    Text Solution

    |

  17. about to only mathematics

    Text Solution

    |

  18. ABC is a right-angled triangle in which angleB=90^(@) and BC=a. If n p...

    Text Solution

    |

  19. If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a ...

    Text Solution

    |

  20. Given that alpha, gamma are roots of the equation Ax^(2)-4x+1=0 and be...

    Text Solution

    |