Home
Class 12
MATHS
The sum 1+3+7+15+31+...to100 terms is 2^...

The sum `1+3+7+15+31+...to100` terms is `2^(100)-102 b` b. `2^(99)-101` c. `2^(101)-102` d. none of these

A

`2^(100)-102`

B

`2^(99)-101`

C

`2^(101)-102`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Here the successive differences are 2,4,8,16,… which are in G.P.
`S=1+3+7+15+31+…+T_(100)`
`=(2^(1)-1)+(2^(2)-1)+(2^(3)-1)+..+(2^(100)-1)`
`=(2+2^(2)+2^(3)+….+2^(100))-100`
`=2((2^(100)-1)/(2-1))-100`
`=2^(101)-102`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Multiple & Comprehension)|66 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise EXERCIESE ( MULTIPLE CORRECT ANSWER TYPE )|2 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.9|9 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

The sum of 20 terms of a series of which every even term is 2 times the term before it, every odd term is 3 times the term before it, the a. (2/7)(6^(10)-1) b. (3/7)(6^(10)-1) c. (3/5)(6^(10)-1) d. none of these

The largest term common to the sequences 1, 11 , 21 , 31 , to100 terms and 31 , 36 , 41 , 46 , to100 terms is 381 b. 471 c. 281 d. none of these

The sum of 50 terms of the series 1+2(1+1/(50))+3(1+1/(50))^2+ is given by 2500 b. 2550 c. 2450 d. none of these

The sum of i-2-3i+4 up to 100 terms, where i=sqrt(-1) is a. 50(1-i) b. 25 i c. 25(1+i) d. 100(1-i)

The sum of rational term in (sqrt(2)+^3sqrt(3)+^6sqrt(5))^(10) is equal to 12632 b. 1260 c. 126 d. none of these

Vector vec c is perpendicular to vectors vec a=(2,-3,1)a n d vec b=(1,-2,3) and satisfies the condition vec c .( hat i+2 hat j-7 hat k)=10. Then vector vec c is equal to a. (7,5,1) b. -7,-5,-1 c. 1,1,-1 d. none of these

The coefficient of x^(53) in the expansion sum_(m=0)^(100)^100C_m(x-3)^(100-m)2^m is (a) 100 C_(47) (b.) 100 C_(53) (c.) -100C_(53) (d.) none of these

The coefficient of x^(49) in the product (x-1)(x-3)(x-99)i s -99^2 b. 1 c. -2500 d. none of these

The minimum value of 2^(x^2-3)^(3+27) is a) 2^(27) (b) 2 (c) 1 (d) none of these

If the sum to infinity of the series 1+2r+3r^2+4r^3+ is 9/4, then value of r is 1//2 b. 1//3 c. 1//4 d. none of these

CENGAGE-PROGRESSION AND SERIES-Exercise (Single)
  1. If the sum of n terms of an A.P is cn (n-1)where c ne 0 then the sum o...

    Text Solution

    |

  2. If bi=1-ai na = Sigma(i=1)^(n) ai, nb = Sigma(i=1)^(n) bi " then " Si...

    Text Solution

    |

  3. The sum 1+3+7+15+31+...to100 terms is 2^(100)-102 b b. 2^(99)-101 c. ...

    Text Solution

    |

  4. Consider the sequence 1,2,2,4,4,4,8,8,8,8,8,8,8,8,... Then 1025th term...

    Text Solution

    |

  5. The value of Sigma(i=1)^(n) Sigma(j=1)^(i) underset(k=1)overset(j) =22...

    Text Solution

    |

  6. If 1^2+2^2+3^2++2003^2=(2003)(4007)(334)a n d(1)(2003)+(2)(2002)+(3)(2...

    Text Solution

    |

  7. If tn denotes the nth term of the series 2+3+6+11+18+….. Then t50 is

    Text Solution

    |

  8. The sum of series Sigma(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is

    Text Solution

    |

  9. If(1^2-t1)+(2^2-t2)+….+(n^2-tn)=(n(n^2-1))/(3) then tn is equal to

    Text Solution

    |

  10. If (1+3+5++p)+(1+3+5++q)=(1+3+5++r) where each set of parentheses cont...

    Text Solution

    |

  11. If Hn=1+12++1/ndot , then the value of Sn=1+3/2+5/3++(99)/(50) is H(50...

    Text Solution

    |

  12. The sum to 50 terms of the series 3/1^2+5/(1^2+2^2)+7/(1^+2^2+3^2)+...

    Text Solution

    |

  13. Let S=4/19+44/(19)^2+444/(19)^3+...oo then find the value of S

    Text Solution

    |

  14. If 1-1/3+1/5-1/7+1/9-1/(11)+=pi/4 , then value of 1/(1xx3)+1/(5xx7)+1/...

    Text Solution

    |

  15. If 1/(1^2)+1/(2^2)+1/(3^2)+ tooo=(pi^2)/6,t h e n1/(1^2)+1/(3^2)+1/(5^...

    Text Solution

    |

  16. lim(nrarroo) Sigma(r=1)^(n) (r)/(1xx3xx5xx7xx9xx...xx(2r+1)) is equal ...

    Text Solution

    |

  17. The greatest interger by which 1+Sigma(r=1)^(30) rxxr ! is divisible...

    Text Solution

    |

  18. If Sigma(r=1)^(n) r^4=I(n), " then "Sigma(r=1)^(n) (2r -1)^4 is equal ...

    Text Solution

    |

  19. Value of (1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))oo is equal to 3 b. 6...

    Text Solution

    |

  20. If x1,x2 …,x(20) are in H.P and x1,2,x(20) are in G.P then Sigma(r=1)^...

    Text Solution

    |