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

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

  • SEQUENCE AND SERIES

    OMEGA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS MCQs|16 Videos

  • SEQUENCE AND SERIES

    OMEGA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS MCQs|16 Videos

  • SAMPLE QUESTIONS PAPER-4 (PUNJAB)

    OMEGA PUBLICATION|Exercise Section- D|7 Videos

  • SETS

    OMEGA PUBLICATION|Exercise Multiple Choice Questions (MCQs)|27 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^2R^n = S^n .

Find the sum of first n terms of an A.P. whose nth term is 3n+1.

If the coefficient of the rth, (r+1)th and (r+2)th terms in the expansion of (1+x)^(n) are in A.P., prove that n^(2) - n(4r +1) + 4r^(2) - 2=0 .

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

Find the sum S_n of the cubes of the first n terms of an A.P. and show that the sum of first n terms of the A.P. is a factor of S_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^(t h) term of a GP are a and b, respectively, and if P is the product of n terms, prove that P^2=(a b)^n .

Prove that sum_(r=0)^n 3^r "^nC_r= 4^n .

In the expansion of (x+a)^n if the sum of odd terms is P and the sum of even terms is Q , then a. P^2-Q^2=(x^2-a^2)^n b. 4P Q=(x+a)^(2n)-(x-a)^(2n) c. 2(P^2+Q^2)=(x+a)^(2n)+(x-a)^(2n) d. none of these

If S_1,S_2,S_3 be the sum of n, 2n, 3n terms of a G.P., show that : S_1(S_3-S_2)= (S_2-S_1)^2 .

OMEGA PUBLICATION-SEQUENCE AND SERIES -IMPORTANT QUESTIONS FROM MISCELLANEOUS EXERCISE
  1. If f(x) is a function satisfying f(x+y)=f(x)f(y) for all xy in n such ...

    Text Solution

    |

  2. The sum of some terms of GP. is 315 whose first term and the common ra...

    Text Solution

    |

  3. The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from t...

    Text Solution

    |

  4. A GP. consists of an even number of terms. If the sum of all the terms...

    Text Solution

    |

  5. If (a+bx)/(a-bx) =(b+cx)/(b-cx) =(c + dx)/(c-dx) (x ne 0), then show t...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. The ratio of the.A.M. and G.M. of two positive numbers a and b is m : ...

    Text Solution

    |

  9. Find the sum to.n terms of the following series 5+ 55 + 555+………..

    Text Solution

    |

  10. Find the sum to n terms 0.6 + 0.66 + 0.666 + ………..

    Text Solution

    |

  11. The sum of first 9 terms of the series (1^(3))/(1)+(1^(3)+2^(3))/(1+3)...

    Text Solution

    |

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

    Text Solution

    |

  13. If S(1), S(2), S(3) are the sum of first n natural numbers, their squa...

    Text Solution

    |

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

    Text Solution

    |

  15. Let S be the sum, P the product and R the sum of reciprocals of n term...

    Text Solution

    |

  16. A farmer, buys a used tractor for Rs.. 12000. He pays Rs.6000 cash and...

    Text Solution

    |

  17. Shamshad Ali buys a scooter for Rs 22000 He pays Rs. 4000 cash And ag...

    Text Solution

    |

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

    Text Solution

    |

  19. Dipesh writes letters to four of his friends. He asks each of them to ...

    Text Solution

    |

  20. Find the sum of the sequence 7, 77, 777, 7777,.....up to n terms.

    Text Solution

    |