Home
Class 11
MATHS
if sn, denotes the sum of n terms of a G...

if `s_n`, denotes the sum of n terms of a GP whose first term and common ratio are `a` and `r` respectively. then `S_1+S_2.........+S_n` is

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise CHECK YOUR UNDERSTANDING|10 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise COMPETITION FILE|21 Videos

  • SEQUENCES AND SERIES

    MODERN PUBLICATION|Exercise EXERCISE|7 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise Chapter Test|11 Videos

  • SETS

    MODERN PUBLICATION|Exercise CHAPTER TEST 1|12 Videos

Similar Questions

Explore conceptually related problems

If S_(n) denotes the sum fo n terms of a G.P. whose first term and common ratio are a and r respectively then show that: S_(1)+S_(3)+S_(5)+……..+S_(2n)-1=(an)/(1-r)-(ar(1-r^(2n)))/((1-r^(2))

Let S_n denote the sum of first n terms of a G.P. whose first term and common ratio are a and r respectively. On the basis of above information answer the following question: The sum of product of first n terms of the G.P. taken two at a time in (A) (r+1)/r S_nS_(n-1) (B) r/(r+1)S_n^2 (C) r/(r+1)S_nS_(n-1) (D) none of these

Let S_n denote the sum of first n terms of a G.P. whose first term and common ratio are a and r respectively. On the basis of above information answer the following question: S_1+S_2+S_2+..+S_n= (A) (na)/(1-r)-(ar(1-^n))/((1-r)^20 (B) (na)/(1-r)-(ar(1+^n))/((1+r)^20 (C) (na)/(1-r)-(a(1-^n))/((1-r)^20 (D) none of these

if S_(n) denotes the sum of n terms of a G.P whose first term is a and common ratio is r then find the sum of S_(1),S_(3),S_(5).........,S_(2)n-1

If S_(1),S_(2),...,S_(n) are the sum of n term of n G.P.whose first term is 1 in each and common ratios are 1,2,3,...,n respectively, then prove that S_(1)+S_(2)+2S_(3)+3S_(4)+...(n-1)S_(n)=1^(n)+2^(n)+3^(n)+...+n^(n)

Prove that the sum of n terms of GP with first term a and common ratio r is given by S_(n)=a(r^(n)-1)/(r-1)

Let S_(n) denote the sum of n terms of an AP whose first term is a.If common difference d is given by d=Sn-kS_(n-1)+S_(n-2), then k is :

If S denotes the sum of an infinite G.P.adn S_(1) denotes the sum of the squares of its terms, then prove that the first term and common ratio are respectively (2SS_(1))/(s^(2)+S_(1)) and (S^(2)-S_(1))/(S^(2)+S_(1))

If S_1,S_2,S_3,...,S_n be the sums of first n terms of n G.P.'s whose first terms are each unity and the common ratios are 1, 2, 3,.....,n respectively, prove that S_1+S_2+2S_3+3S_4+.........+(n-1)S_n=1^n+2^n+3^n+....+n^n.

MODERN PUBLICATION-SEQUENCES AND SERIES-REVESION EXERCISE
  1. If mth, nth and pth terms of a G.P. form three consecutive terms of a ...

    Text Solution

    |

  2. If x,y,z are in G.P and a^x=b^y=c^z,then

    Text Solution

    |

  3. We are given two G.P's one with the first term a and common ratio r an...

    Text Solution

    |

  4. if sn, denotes the sum of n terms of a GP whose first term and common ...

    Text Solution

    |

  5. If p, q, r are in G.P. and the equations, p x^2+2q x+r=0and dx^2+2e x...

    Text Solution

    |

  6. If S(n) denotes the sum of n terms of a G.P., prove that: (S(10)-S(20)...

    Text Solution

    |

  7. The sum of the first thre consecutive terms of G.P is 13 and the sum o...

    Text Solution

    |

  8. If 1/(a+b)+1/(b+c)=1/b, prove that a,b,c are in G.P.

    Text Solution

    |

  9. 150 workers were engaged to finish a job in a certain number of days. ...

    Text Solution

    |

  10. If |x|<1a n d|y|<1, find the sum of infinity of the following series: ...

    Text Solution

    |

  11. A manufacture reckons that the value of a machine which costs him Rs. ...

    Text Solution

    |

  12. The sum of the series : 1+1/(1+2)+1/(1+2+3)+...... upto 10 terms is :

    Text Solution

    |

  13. Find the sum of the series: 1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.

    Text Solution

    |

  14. Obtain the sum of the series 1/4+1/16+1/64……………….to oo

    Text Solution

    |

  15. Show that (1xx2^2+2xx3^2+dotdotdot+nxx(n+1)^2)/(1^2xx2+2^2xx3+dotdotdo...

    Text Solution

    |

  16. What will Rs. 500 amounts to in 10 years after its deposit in a bank w...

    Text Solution

    |

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

    Text Solution

    |

  18. If a1,a2,a3, ,an are in A.P., where ai >0 for all i , show that 1/(sqr...

    Text Solution

    |

  19. if S is the sum , P the product and R the sum of reciprocals of n term...

    Text Solution

    |

  20. A thief runs with a uniform speed of 100 m/min. After one minute a pol...

    Text Solution

    |