Home
Class 12
MATHS
If x=sum(n=0)^ooa^n , y=sum(n=0)^oob^n ,...

If `x=sum_(n=0)^ooa^n , y=sum_(n=0)^oob^n , z=sum_(n=0)^ooc^n , w h e r e ra ,b ,a n dc` are in A.P. and `|a|<,|b|<1,a n d|c|<1,` then prove that `x ,ya n dz` are in H.P.

A

HP

B

Arithmetic -Geometric Progression

C

AP

D

GP

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Exercise O-3|1 Videos

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Exercise O-4|1 Videos

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Exercise O-1|1 Videos

  • RACE

    ALLEN|Exercise Race 21|14 Videos

  • TEST PAPER

    ALLEN|Exercise CHEMISTRY SECTION-II|3 Videos

Similar Questions

Explore conceptually related problems

If x=sum_(n=0)^(oo) a^(n),y=sum_(n=0)^(oo)b^(n),z=sum_(n=0)^(oo)(ab)^(n) , where a,blt1 , then

If a,b,c are proper fractiion are in H.P. and x sum_(n=1)^oo a^n, y=sum_(n=1)^oo b^n, z= sum_(n=1)^oo c^n then x,y,z are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If x=sum_(n=0)^oocos^(2n)theta,y=sum_(n=0)^oosin^(2n)varphi,z=sum_(n=0)^oocos^(2n)thetasin^(2n)varphi,w h e r e0 < theta,varphi < pi//2 prove that x z+y z-z=x ydot

If x=sum_(n=0)^oocos^(2n)theta,y=sum_(n=0)^oosin^(2n)varphi,z=sum_(n=0)^oocos^(2n)thetasin^(2n)varphi , where 0lttheta,varphi ltpi//2 prove that x z+y z-z=x ydot

"For "0ltthetalt(pi)/(2) , if x=sum_(n=0)^(oo)cos^(2n)theta,y=sum_(n=0)^(oo)sin^(2n)phi,z=sum_(n=0)^(oo)cos^(2n)thetasin^(2n)phi , then

If x = underset(n-0)overset(oo)sum a^(n), y= underset(n =0)overset(oo)sum b^(n), z = underset(n =0)overset(oo)sum C^(n) where a,b,c are in A.P. and |a| lt 1, |b| lt 1, |c| lt 1 , then x,y,z are in

sum_(n=0)^(oo) ((log_ex)^n)/(n!)

If S_n=sum_(r=0)^n 1/(nC_r) and t_n=sum_(r=0)^n r/(nC_r), then t_n/S_n=

Let x= sum_(n=0)^oo (-1)^n (tantheta)^(2n) and y = sum_(n=0)^oo (costheta)^(2n) qhere theta in (0,pi/4) , then

If a_n=sum_(r=0)^n1/(nC_r), then sum_(r=0)^n r/(nC_r) equals

ALLEN-SEQUENCE AND PROGRESSION-Exercise O-2
  1. If a, b, c are in AP, then (a - c)^(2) equals

    Text Solution

    |

  2. If for an A.P. a1,a2,a3,........,an,........a1+a3+a5=-12 and a1a2a3=8,...

    Text Solution

    |

  3. If the sum of the first 11 terms of an arithmetical progression equals...

    Text Solution

    |

  4. Let s(1), s(2), s(3).... and t(1), t(2), t(3).... are two arithmetic s...

    Text Solution

    |

  5. If x ∈ R and the numbers (5 ^ (1−x) +5^ (x+1) , a/2, (25^ x +25^ −x ...

    Text Solution

    |

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

    Text Solution

    |

  7. In an A.P. with first term 'a' and the common difference d(a, d!= 0), ...

    Text Solution

    |

  8. Let an, n in N is an A.P with common difference d and all whose terms ...

    Text Solution

    |

  9. Let a(1), a(2),…. and b(1),b(2),…. be arithemetic progression such tha...

    Text Solution

    |

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

    Text Solution

    |

  11. If (1 + 3 + 5 + .... " upto n terms ")/(4 + 7 + 10 + ... " upto n term...

    Text Solution

    |

  12. If a != 1 and l n a^(2) + (l n a^(2))^(2) + (l n a^(2))^(3) + ... = 3 ...

    Text Solution

    |

  13. The sum of the first three terms of an increasing G.P. is 21 and the s...

    Text Solution

    |

  14. a, b, c are distinct positive real in HP, then the value of the expres...

    Text Solution

    |

  15. An H.M. is inserted between the number 1/3 and an unknown number. If w...

    Text Solution

    |

  16. If abcd = 1, where a,b,c and d are positive real numbers, then find th...

    Text Solution

    |

  17. If 27 abc>= (a+b+c)^3 and 3a +4b +5c=12 then 1/a^2+1/b^3+1/c^5=10, w...

    Text Solution

    |

  18. If x=sum(n=0)^ooa^n , y=sum(n=0)^oob^n , z=sum(n=0)^ooc^n , w h e r e ...

    Text Solution

    |