Home
Class 12
MATHS
Value of lim(ntooo)(1+1/3)(1+1/(3^2))(1+...

Value of `lim_(ntooo)(1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))oo` is equal to `3` b. `6/5` c. `3/2` d. none of these

A

3

B

`6/5`

C

`3/2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Consider the first product,
`P=(1+1/3)(1+1/3^(2))(1+1/3^(4))(1+1/3^(8))..(1+1/(3^(2^(n))))`
`=((1+1/3)(1+1/3^(2))(1+1/3^(4))(1+1/3^(8))...(1+1/3^(2^(n))))/((1-1/3))`
`=((1+1/3^(2))(1+1/3^(2))(1+1/3^(4))(1+1/3^(8))...(1+1/3^(2^(n))))/((1-1/3))`
`=((1+1/3^(4))(1+1/3^(4))(1+1/3^(8))...(1+1/3^(2^(n))))/((1-1/3))`
`1/((1-1/3))(1-(1/3)^(2^(n-1)))`
`=3/2(1-(1/3)^(2^(n+1)))`
`rArr(1+1/3)(1+1/3^(2))(1+1/3^(4))(1+1/3^(8))...` infinity
`=lim_(ntooo)3/2(1-(1/3)^(2^(n+1)))=3/2`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise EXERCIESE ( MULTIPLE CORRECT ANSWER TYPE )|66 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise EXERCIESE ( LINKED COMPREHENSION TYPE )|60 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.9|9 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

Value of (1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))........oo is equal to a. 3 b. 6/5 c. 3/2 d. none of these

(lim)_(ntooo)sum_(r=1)^n r/(1xx3xx5xx7xx9xx.....xx(2r+1)) is equal to 1/3 b. 3/2 c. 1/2 d. none of these

The reciprocal of the value of: lim_(n->oo)(1-1/(2^2))(1-1/(3^2))(1-1/(4^2))(1-1/(n^2))i s

1+1/(3!)+1/(5!)+1/(7!)+......oo is equal to

1+3^2/(2!)+3^4/(4!)+3^6/(6!)+......oo is equal to

lim_(xtooo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo (c) 1/2 (d) none of these

lim_(n->oo)(-3n+(-1)^n)/(4n-(-1)^n) is equal to a. -3/4 b. 0 if n is even c. -3/4 if n is odd d. none of these

lim_(n->oo){1/(1-n^2)+2/(1-n^2)+......n/(1-n^2)} is equal to (a) 0 (b) -1/2 (c) 1/2 (d) none of these

The lim_(x to oo) ((3x-1)/(3x+1))^(4x) equals

Evaluate lim_(ntooo) (1^(3)+2^(3)+3^(3)+...+n^(3))/(sqrt(4n^(8)+1)).

CENGAGE PUBLICATION-PROGRESSION AND SERIES-EXERCIESE ( SINGLE CORRECT ANSWER TYPE )
  1. Consider the sequence 1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,... Then 1025th te...

    Text Solution

    |

  2. The value of sum(i-1)^nsum(j=1)^isum(k=1)^j1=220 , then the value of n...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. Let S=4/(19)+(44)/(19^2)+(444)/(19^3)+ u ptooo . Then s is equal to a....

    Text Solution

    |

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

    Text Solution

    |

  12. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Value of lim(ntooo)(1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))oo is equal...

    Text Solution

    |

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

    Text Solution

    |

  18. The value of Sigma(r=1)^(n) (a+r+ar)(-a)^r is equal to

    Text Solution

    |

  19. The sum of series x/(1-x^2)+(x^2)/(1-x^4)+(x^4)/(1-x^8)+ to infinite t...

    Text Solution

    |

  20. The sum of 20 terms of the series whose rth term s given by kT(n)=(-1)...

    Text Solution

    |