Home
Class 11
MATHS
Sum the series : (1+x)+(1+x+x^(2))+(1+x+...

Sum the series : `(1+x)+(1+x+x^(2))+(1+x+x^(2)+x^(3))+……` up to n terms

Text Solution

Verified by Experts

The correct Answer is:
`=(1)/(1-x)[n-(x^(2)(1-x^(n)))/(1-x)]`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM, SEQUENCES AND SERIES

    FULL MARKS|Exercise EXERCISE 5.5|20 Videos

  • BASIC ALGEBRA

    FULL MARKS|Exercise Exercise-2.13|20 Videos

  • COMBINATORICS AND MATHEMATICAL INDUCTION

    FULL MARKS|Exercise ADDITIONAL QUESTIONS|33 Videos

Similar Questions

Explore conceptually related problems

The sum of first n terms of the series 1 + (1 + x) y+ (1 + x + x^(2)) y^(2) + (1 + x + x^(2) + x^(3))y^(3) + ……….. is

The sum of series x/(1-x^2)+(x^2)/(1-x^4)+(x^4)/(1-x^8)+ to infinite terms, if |x|<1, is

The sum of series 1 + 2x + 3x^(2) + 4x^(3) + ...... up to infinity when x lies between 0 and 1 i.e., 0 lt x lt 1 is

Expand (1+x)^(2/3) up to four terms for |x|lt1

If the sum to infinty of the series , 1+4x+7x^(2)+10x^(3)+…. , is (35)/(16) , where |x| lt 1 , then 'x' equals to

The sum of the polynomials p(x) = x^(3) - x^(2) - 2, q(x) = x^(2) - 3x + 1

(3x - 9)/( (x - 1 )(x + 2 )(x^(2)+1))

By using properties of determinants , show that : {:[( 1,x,x^(2) ),( x^(2) ,1,x) ,( x,x^(2), 1) ]:} =( 1-x^(3)) ^(2)

FULL MARKS-BINOMIAL THEOREM, SEQUENCES AND SERIES -Additional Questions Solved
  1. Find the 18^(th) and 25^(th) terms of the sequence defined by a(n)=...

    Text Solution

    |

  2. Write the first six terms of the sequences given by (i) a(1)=a(2)...

    Text Solution

    |

  3. An A.P. consists of 21 terms. The sum of the three terms in the middle...

    Text Solution

    |

  4. Prove that the product of the 2^(nd) and 3^(rd) terms of an arithmetic...

    Text Solution

    |

  5. If the p^(th), q^(th) and r^(th) terms of an A.P. are a, b, c respecti...

    Text Solution

    |

  6. If a, b, c are in A.P. and p is the A.M. between a and b and q is the ...

    Text Solution

    |

  7. If x, y, z be respectively the p^(th), q^(th) and r^(th) terms of a G....

    Text Solution

    |

  8. If the ratio of the sums of m terms and n terms of an A.P. be m^(2) : ...

    Text Solution

    |

  9. Determine the number of terms of geometric progression {a(n)} if a(1)=...

    Text Solution

    |

  10. The sum of first three terms of a G.P. is to the sum of the first six ...

    Text Solution

    |

  11. Find the sum to n term the series : (x+y)+(x^(2)+xy+y^(2))+(x^(3)+x^(2...

    Text Solution

    |

  12. Sum the series : (1+x)+(1+x+x^(2))+(1+x+x^(2)+x^(3))+…… up to n terms

    Text Solution

    |

  13. Sum up to n terms the series : 7+77+777+7777+…..

    Text Solution

    |

  14. If S(1), S(2), S(3) be respectively the sums of n, 2n, 3n, terms of a ...

    Text Solution

    |

  15. If sum of the n terms of a G.P be S, their product P and the sum of th...

    Text Solution

    |

  16. Find the root(3)(126) approximately to two decimal places.

    Text Solution

    |

  17. Write the first four terms in the expansions of the following : (i...

    Text Solution

    |

  18. Evaluate the following : (i) root(3)(1003) correct to 4 places of...

    Text Solution

    |

  19. If x so large prove that sqrt(x^(2)+25)-sqrt(x^(2)+9)=(8)/(x) nearly.

    Text Solution

    |

  20. Show that x^(n)=1+n(1-(1)/(x))+(n(n+1))/(1.2)(1-(1)/(x))^(2)+….

    Text Solution

    |