Home
Class 11
MATHS
If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo...

If `x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n dz=c+c/(r^2)+c/(r^4)+oo,` prove that `(x y)/z=(a b)/c`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    RD SHARMA ENGLISH|Exercise All Questions|200 Videos

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    RD SHARMA ENGLISH|Exercise All Questions|22 Videos

Similar Questions

Explore conceptually related problems

If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n d z=c+c/(r^2)+c/(r^4)+oo, prove that (x y)/z=(a b)/c

"If "x=a+(a)/(r)+(a)/(r^(2))+...oo,y=b-(b)/(r)+(b)/(r^(2))-...oo,"and "z=c+(c)/(r^(2))+(c)/(r^(4))+...oo," then prove that "(xy)/(z)=(ab)/(c).

If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x^(2) + y^(2) + z^(2) = r^(2)

If A=1+r^a+r^(2a)+ to oo and B=1+r^b+r^(2b)+oo , prove that r=((A-1)/A)^(1//a)=((B-1)/B)^(1//b)

If x=1+a+a^2+oo,w h e r e|a|<1a n dy=1+b+b^2+oo,w h e r e|b|<1. prove that: 1+a b+a^2b^2+oo=(x y)/(x+y-1)

If a = sum_(r=1)^(oo) 1/(r^(2)), b = sum_(r=1)^(oo) 1/((2r-1)^(2)), then (3a)/b is equal to _____

If ^nP_(r-1):^nPr: ^nP_(r+1)=a,b:c, prove that b^2=a(b+c)

If a=x y^(p-1),\ b=x y^(q-1) and c=x y^(r-1) , prove that a^(q-r)b^(r-p)\ c^(p-q)=1

If sum_(r=1)^(oo) (C^r)/(r!) =1 then C =

If r_(1), r_(2) ,r_(3) are the ex-radii of DeltaABC, then prove that (bc)/(r_(1))+(ca)/(r _(2))+(ab)/(r _(3))=2R [((a)/(b)+(b)/a)+((b)/(c)+(c)/(b))+((c)/(a)+ (a)/(c))-3]

RD SHARMA ENGLISH-GEOMETRIC PROGRESSIONS-All Questions
  1. After striking a floor a certain ball rebounds (4/5)^(t h) of the heig...

    Text Solution

    |

  2. Sum the following geometric series to infinity: 1/2+1/(3^3)+1/(2^3)+1/...

    Text Solution

    |

  3. If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n dz=c+c/(r^2)+c/(r^4)+oo, ...

    Text Solution

    |

  4. If x=1+a+a^2+oo,w h e r e|a|<1a n dy=1+b+b^2+oo,w h e r e|b|<1. prove...

    Text Solution

    |

  5. If A=1+r^a+r^(2a)+ to oo and B=1+r^b+r^(2b)+oo , prove that r=((A-1)/A...

    Text Solution

    |

  6. Prove that the product n geometric means between two quantities is equ...

    Text Solution

    |

  7. If a ,b ,c ,d are four distinct positive numbers in G.P. then A. a +...

    Text Solution

    |

  8. Find the value of n so that (a^(n+1)+b^(n+1))/(a^n+b^n)may be the geo...

    Text Solution

    |

  9. Insert 5 geometric means between 576 and 9.

    Text Solution

    |

  10. Let x be the arithmetic mean and y ,z be tow geometric means between a...

    Text Solution

    |

  11. Find two positive numbers whose difference is 12 an whose A.M. exce...

    Text Solution

    |

  12. If one geometric mean G and two arithmetic means A1a n dA2 be inserted...

    Text Solution

    |

  13. If a is the A.M. of b and c and the two geometric means are G1 and G2...

    Text Solution

    |

  14. If x in R , find the minimum value of the expression 3^x+3^(1-x)dot

    Text Solution

    |

  15. If x ,y ,z are distinct positive numbers, then prove that (x+y)(y+z)(z...

    Text Solution

    |

  16. If a ,b ,c are in G.P. then prove that (a^2+a b+b^2)/(b c+c a+a b)=(b+...

    Text Solution

    |

  17. If 1/(a+b),1/(2b),1/(b+c) are three consecutive terms of an A.P., prov...

    Text Solution

    |

  18. If a ,b ,c ,d are in G.P. prove that: (a b-c d)/(b^2-c^2)=(a+c)/b

    Text Solution

    |

  19. If a ,b ,c ,d are in G.P. prove that: (a^2+b^2),(b^2+c^2),(c^2+d^2) ar...

    Text Solution

    |

  20. The sum of three numbers a ,b ,c in A.P. is 18 . If aa n db are eac...

    Text Solution

    |