Home
Class 12
MATHS
The A.M. of the series 1, 2, 4, 8, 16,.....

The A.M. of the series `1, 2, 4, 8, 16,.....,2^n` is -

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
The required AM is
`overline(X)=(1+2+2^(2)+2^(3)+..+2^(n))/(n+1)=((2^(n+1)-1))/((n+1)(2-1))=(2^(n+1)-1)/(n+1)`
Promotional Banner

Topper's Solved these Questions

  • STATISTICS

    CENGAGE ENGLISH|Exercise Archives|10 Videos

  • STATISTICS

    CENGAGE ENGLISH|Exercise Exercise 11.2|6 Videos

  • SOLUTIONS AND PROPERTIES OF TRIANGLE

    CENGAGE ENGLISH|Exercise Comprehension Type|6 Videos

  • STRAIGHT LINE

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|8 Videos

Similar Questions

Explore conceptually related problems

The geometric mean of the series 1,2,4,8,16,....,2^n is

Statement-1 :The A.M. of series 1,2,4,8,16,…… 2^n is (2^(n+1)-1)/(n+1) Statement-2 : Arithmetic mean (A.M.) of ungrouped data is (Sigmax_i)/n where x_1,x_2 …. x_n are n numbers .

Find the n^(th) term of the series : 1,2,4,8, . . . . . . . . .

If A.M., G.M., and H.M. of the first and last terms of the series of 100 , 101 , 102 ,...(n-1),n are the terms of the series itself, then the value of n is (100ltnlt500)

If A.M., G.M., and H.M. of the first and last terms of the series of 100 , 101 , 102 ,...n-1,n are the terms of the series itself, then the value of ni s(100

The A.M. of the series .^(n)C_(0), .^(n)C_(1), .^(n)C_(2),….,.^(n)C_(n) is

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

Write the sum of the series 2+4+6+8+...........+2n

Sum the series to infinity : 16 ,-8,4 , .....

The sum to infinity of the series 1/2.4+1/4.6+1/6.8+1/8.10+....... is

CENGAGE ENGLISH-STATISTICS-Exercises
  1. Coefficients of variation of two distributions are 50 and 60, and thei...

    Text Solution

    |

  2. The mean of a set of numbers is overline(X). If each number is divided...

    Text Solution

    |

  3. The A.M. of the series 1, 2, 4, 8, 16,.....,2^n is -

    Text Solution

    |

  4. The mean of n items is overline(X). If the first item is increased by ...

    Text Solution

    |

  5. For a slightly asymmetric distribution, mean and medain are 5 and 6, r...

    Text Solution

    |

  6. For a normal distribution if the mean is M, mode is M(0) and median is...

    Text Solution

    |

  7. The following data give the distribution of heights of students : {:...

    Text Solution

    |

  8. An automobile driver travels from a plain to a hill station 120 km awa...

    Text Solution

    |

  9. The mean deviation of the data 3,10,10,4,7,10,5 from the mean is

    Text Solution

    |

  10. when tested the lives (in hours) of 5 bulbs were noted as follows 13...

    Text Solution

    |

  11. Following are the marks obtained by 9 student in a mathematics test ...

    Text Solution

    |

  12. If the mean of the distribution is 2.6, then the value of y is {:("V...

    Text Solution

    |

  13. If the mean of the set of numbers x1,x2, x3, ..., xn is barx, then the...

    Text Solution

    |

  14. The harmonic mean of 4,8,16 is

    Text Solution

    |

  15. The average of n numbers x(1),x(2),x(3),..,x(n) is M. If x(n) is repla...

    Text Solution

    |

  16. The following data gives the distribution of height of students : {:...

    Text Solution

    |

  17. For a slightly asymmetric distribution, mean and medain are 5 and 6, r...

    Text Solution

    |

  18. Runs scored by a batsman in 10 innings are : 38, 70,48,34,42,55,63,46,...

    Text Solution

    |

  19. If mu the mean of distribution (y(i),f(i)), then sum f(i)(y(i)-mu)=

    Text Solution

    |

  20. The range of the following set of observations 2,3,5,9, 8, 7, 6, 5, 7,...

    Text Solution

    |