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

  • SEQUENCES AND SERIES

    JBD PUBLICATION|Exercise EXAMPLE|54 Videos
  • RELATIONS AND FUNCTIONS

    JBD PUBLICATION|Exercise EXAMPLE|35 Videos
  • SETS

    JBD PUBLICATION|Exercise EXAMPLE|58 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 .

JBD PUBLICATION-SEQUENCES AND SERIES-EXAMPLE
  1. The sum of three numbers which are consecutive terms of an A.P. is 21....

    Text Solution

    |

  2. If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c...

    Text Solution

    |

  3. Find a G.P. for which sum of the first two terms is -4 and the fifth t...

    Text Solution

    |

  4. The sum of an inifinite G.P. is 8. If the second term is 2, then find ...

    Text Solution

    |

  5. Find the sum to n terms of the series 3 xx 8 + 6 xx 11 + 9 xx 14 + …

    Text Solution

    |

  6. Find the sum of the series 1*n+2*(n-1)+3*(n-2)+4*(n-3)+"..."+(n-1)*2+n...

    Text Solution

    |

  7. The difference between any two consecutive interior angles of a polygo...

    Text Solution

    |

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

    Text Solution

    |

  9. If A.M and G.M of two positive numbers are 13 and 12 respectively. Fin...

    Text Solution

    |

  10. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

    Text Solution

    |

  11. The ratio of the sums of m and n terms of an A.P. is m^2: n^2. Show th...

    Text Solution

    |

  12. If a^(2),b^(2),c^(2) are in A.P. Prove that (a)/(b+c),(b)/(c+a),(c)/(a...

    Text Solution

    |

  13. If S(1),S(2),S(3)be respectively the sum of n, 2n and 3n terms of a GP...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. The sum of two numbers is 6 times their geometric mean, show that numb...

    Text Solution

    |

  17. The sum of two numbers is 6 times their geometric mean, show that numb...

    Text Solution

    |

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

    Text Solution

    |

  19. If a,b,c are in G.P. and x,y are the arithmetic means of a,b and b,c r...

    Text Solution

    |

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

    Text Solution

    |