Home
Class 11
MATHS
Sum of the first n terms of the series 1...

Sum of the first `n` terms of the series `1/2+3/4+7/8+(15)/(16)+.........` is equals to (a).`2^n-n-1` (b). `1-2^(-n)` (c). `n+2^(-n)-1` (d). `2^n+1`

A

`2(n-1)+(1)/(2n-1)`

B

`2n-(1)/(2^(n))`

C

`2+(1)/(2^(n))`

D

`2n-1+(1)/(2^(n))`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|129 Videos

  • QUADRATIC EXPRESSIONS AND EQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos

  • SETS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

find the sum of n terms of the series (4-1/n)+(4-2/n)+(4-3/n)+...........

Sum to n-terms of the series (1/2)^2 + (3/4)^2 + (7/8)^2 + (15/16)^2 +…. Is given by :

Sum of n terms of the series (2n-1)+2(2n-3)+3(2n-5)+... is

The sum of the series 2/3+8/9+(26)/(27)+(80)/(81)+ to n terms is (a) n-1/2(3^(-n)-1) (b) n-1/2(1-3^(-n)) (c) n+1/2(3^n-1) (d) n-1/2(3^n-1)

If S_n=sum_(r=1)^n(1+2+2^2+ .......+2^r)/(2^r), then S_n is equal to (a) 2^n n-1 (b) 1-1/(2^n) (c) n -1+1/(2^n) (d) 2^n-1

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

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

Sum to n terms of the series :1 + 2 (1 + (1)/(n)) + 3 (1 + (1)/(n )) ^(2) + ………

Find the sum of n terms \ of the series: 1/(1. 2)+1/(2. 3)+1/(3. 4)+...............+1/(n.(n+1))

The sum of n terms of the series 5/1.2.1/3+7/2.3.1/3^2+9/3.4.1/3^3+11/4.5.1/3^4+.. is (A) 1+1/2^(n-1).1/3^n (B) 1+1/(n+1).1/3^n (C) 1-1/(n+1).1/3^n (D) 1+1/2n-1.1/3^n

OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Chapter Test
  1. The sum of the integers from 1 to 100 which are not divisible by 3 or ...

    Text Solution

    |

  2. Let the harmonic mean and geometric mean of two positive numbers be in...

    Text Solution

    |

  3. The sum of the series 1 + 2.2+ 3.2^(2) + 4.2^(3) + 5.2^(4) + ….. +...

    Text Solution

    |

  4. If a\ (1/b+1/c),\ b(1/c+1/a),\ c(1/a+1/b) are in A.P. prove that a ,\ ...

    Text Solution

    |

  5. If the m^(th),n^(th)andp^(th) terms of an A.P. and G.P. be equal and b...

    Text Solution

    |

  6. The 7th term of a H.P. is (1)/(10) and 12 th term is (1)/(25), find th...

    Text Solution

    |

  7. The length of side of a square is 'a' metre. A second square is formed...

    Text Solution

    |

  8. The harmonic mean of the roots of the equation (5+sqrt(2))x^2-(4+sqrt(...

    Text Solution

    |

  9. If three positive real numbers a,b,c, (cgta) are in H.P., then log(a+c...

    Text Solution

    |

  10. In an A.P., the p^(th) term is 1/q and the q^(th) term is 1/p. fin...

    Text Solution

    |

  11. The sum of the series 2/3+8/9+(26)/(27)+(80)/(81)+ to n terms is (a) n...

    Text Solution

    |

  12. If a,b,c are in H.P. , then

    Text Solution

    |

  13. The odd value of n for which 704+1/2(704)+… upto n terms = 1984-1/2(1...

    Text Solution

    |

  14. The positive interger n for which 2xx2^2+3xx 2^3+4xx2^4+….+nxx2^4=2^(n...

    Text Solution

    |

  15. If 1^2+2^2+3^2++2003^2=(2003)(4007)(334) and (1)(2003)+(2)(2002)+(3)(2...

    Text Solution

    |

  16. The sum to n terms of the series (n^(2)-1^(2))+2(n^(2)-2^(2))+3(n^(2...

    Text Solution

    |

  17. The sum of the series a-(a+d)+(a+2d)-(a+3d)+... up to (2n+1) terms is:...

    Text Solution

    |

  18. If Hn=1+1/2+...+1/ndot , then the value of Sn=1+3/2+5/3+...+(99)/(50) ...

    Text Solution

    |

  19. Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............

    Text Solution

    |

  20. If a(n)=1+(1)/(2)+(1)/(3)+(1)/(4)+(1)/(5)+ . . . .+(1)/(2^(n)-1), then

    Text Solution

    |