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

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`

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    V PUBLICATION|Exercise QUESTIONBANK|79 Videos
  • SETS

    V PUBLICATION|Exercise QUESTION BANK|116 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. Then prove that P^2R^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

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 .

Consider the G.p 3, 6, 12…If the sum to n terms is 381, find n

If S_1,S_2 and S_3 are respectively the sums of n, 2n and 3n terms of an AP.Prove that S_3=3(S_2-S_1)

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

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 .

The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the C.R of the G.P

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. 1,-a,a^2,-a^3,...(ane-1)

V PUBLICATION-SEQUENCES AND SERIES-QUESTIONBANK
  1. The sum of the first four terms of an A.Pis 56. The sum of the last fo...

    Text Solution

    |

  2. If (a+b x)/(a-b x)=(b+c x)/(b-c x)=(c+d x)/(c-d x)(x ne 0), then show ...

    Text Solution

    |

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

    Text Solution

    |

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

    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 ...

    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...

    Text Solution

    |

  7. If a and b are the roots of x^2-3 x+p=0 and c and d are roots of x^2-1...

    Text Solution

    |

  8. If A and G be A. M and G. M respectively between two positive numbers....

    Text Solution

    |

  9. 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....

    Text Solution

    |

  10. Find the sum to n terms of the series: 5+55+555+………..

    Text Solution

    |

  11. Find the 20^( th) term of the series 2 xx 4+4 xx 6+6 xx 8+. . .,+ n t...

    Text Solution

    |

  12. Find the sum of the first n terms of the series : 3+7+13+21+31+. . .

    Text Solution

    |

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

    Text Solution

    |

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

    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

    |