Home
Class 11
MATHS
Let S be the sum P the product and R the...

Let S be the sum P the product and R the sum of reciprocals of n terms in a G.P. Then prove that `P^2R^n=S^n`

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|83 Videos
  • SETS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|268 Videos

Similar Questions

Explore conceptually related problems

Let S be the sum, P , the product and R the sum of reciprocals of n terms in a G . P . Prove that P^2 R^n=S^n

If the first and the n^(th) terms of a G.P. are a and b respectively and if p is the product of n terms, prove that p^2=(ab)^n

Show that the ratio of the sum of first n terms of a G.P.to the sum of terms from (n+1)^(th) to (2n)^(th) term is 1/r^n

If the first and the n^( th) term of a . G . P are a and b , respectively, and if P is the product of n terms, prove that P^2=(a b)^n .

Find the sum to n terms of the G.P. x^3,x^5,x^7,…(xne+-1)

In an increasing G.P. the sum of the first and last term is 66 the product of the second and the last terms is 128 and the sum of the terms is 126 . Then number of terms in the series is .

Show that the ratio of the sum of first n terms of a G. P to the sum of, terms from (n+1)^ (th) to. (2 n)^(th) term is 1/(r^n) .

Consider an infinite G.P with first term a and common ratio r,(-1ltrlt1) If the sum of the given infinite G.P is 15 and the sum of squares of its terms is 45, find a and r

Find the sum to n terms of the G.P. sqrt7,sqrt21,3sqrt7…

Let S_(n) denote the sum of first n terms of an A.P . If S_(2n) = 3S_(n) then find the ratio S_(3n)//S_(n) .

A N EXCEL PUBLICATION-SEQUENCES AND SERIES-QUESTION BANK
  1. The sum of the first 4 terms of an A.P. is 56. The sum of the last 4 t...

    Text Solution

    |

  2. If (a+bx)/(a-bx)=(b+cx)/(b-cx)=(c+dx)/(c-dx)(xne0) then show that a,b,...

    Text Solution

    |

  3. Let S be the sum P the product and R the sum of reciprocals of n terms...

    Text Solution

    |

  4. The p^(th),q^(th)and r^(th) terms of an A.P. are a,b,c respectively. S...

    Text Solution

    |

  5. If a (1/b+1/c),b(1/c+1/a),c(1/a+1/b) are in A.P. prove that a,b,c are ...

    Text Solution

    |

  6. If a,b,c,d are in G.P. prove that (a^n+b^n),(b^n+c^n),(c^n+d^n) are in...

    Text Solution

    |

  7. If a and b are the roots of x^2-3x+p=0 and c,d are the roots of x^2-12...

    Text Solution

    |

  8. If a,b,c are in A.P. b,c,d are in G.P. and 1/c,1/d,1/e are in A.P. pro...

    Text Solution

    |

  9. Find sum of 5 + 55 + 555 + ... to n terms.

    Text Solution

    |

  10. Find the sum of the following series upto n terms 0.6+0.66+0.666+…

    Text Solution

    |

  11. Find the 20^(th) term of the series 2xx4+4xx6+6xx8+… to n terms

    Text Solution

    |

  12. Find the sum of the 1^(st) n terms of the series 3+7+13+21+31+…

    Text Solution

    |

  13. If S1.S2.S3 are the sum of the first n natural numbers, their squares ...

    Text Solution

    |

  14. Find the sum of the following series upto n terms (1^3)/1+(1^3+2^3)/(1...

    Text Solution

    |

  15. Show that (1 xx 2^2+2 xx 3^2+. .+n xx(n+1)^2)/(1^2 xx 2+2^2 xx 3+. .+n...

    Text Solution

    |

  16. A farmer buys a used tractor for Rs. 12,000. He pays Rs. 6000 cash and...

    Text Solution

    |

  17. Shamshad Ali buys a Scooter for Rs. 22000. He pays Rs. 4000 cash and a...

    Text Solution

    |

  18. A person writes a letter to four of his friends. He asks each one of t...

    Text Solution

    |

  19. A man deposited Rs. 10000 in a bank at the rate of 5% simple interest ...

    Text Solution

    |

  20. A manufacturer reckons that the value of a machine, which costs him Rs...

    Text Solution

    |