Home
Class 14
MATHS
Sum of n terms of the series loga + l...

Sum of n terms of the series
`log_a + log((a^2)/(b)) + log((a^3)/(b^2)) + log ((a^4)/(b^3)) + ...` is :

A

`log{a^n/b^(n-1)}^(n//2)`

B

`log{a^(n+1)/b^(n-1)}^(n//2)`

C

`log{a^n/b^n}^(n//2)`

D

`log{a^(n+1)/b^n}^(n//2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • RATIO, PROPORTION & VARIATION

    QUANTUM CAT|Exercise QUESTION BANK|238 Videos
  • SET THEORY

    QUANTUM CAT|Exercise QUESTION BANK|81 Videos

Similar Questions

Explore conceptually related problems

Find the sum of n terms of the series log a+log((a^(2))/(b))+log((a^(3))/(b^(2)))+log((a^(4))/(b^(3)))

Show that the sequence log a,log((a^(2))/(b)),log((a^(3))/(b^(2))),log((a^(4))/(b^(3))) forms an A.P.

The sequence log((a)/(b)),log((a^(2))/(b^(2))),log((a^(3))/(b^(3)))......... is

The sum of the series log_(a)b+log_(a^(2))b^(2)+log_(a^(3))b^(3)+....log_(a^(n))b^(n)

Find the sum of 'n' terms of the series. log_(2)(x/y) + log_(4)(x/y)^(2) + log_(8)(x/y)^(3) + log_(16)(x/y)^(4) +……..

log_(e^(2))^(a^(b))*log_(a^(3))^(b^(c))log_(b^(4))^(e^(a))

Simplify log(a^(2)times b^(3))-log((a^(3))/(b^(2)))

QUANTUM CAT-SEQUENCE, SERIES & PROGRESSIONS-QUESTION BANK
  1. What is the sum of n terms of the series -1 + 1^2 - 2 + 2^2 - 3 + 3^2 ...

    Text Solution

    |

  2. Find the sum of 1+2/3+4/9+6/27+8/81+10/243+....+oo:

    Text Solution

    |

  3. Sum of n terms of the series loga + log((a^2)/(b)) + log((a^3)/(b^2...

    Text Solution

    |

  4. If a1 , a2 , a3, …."" an are in A.P. where ai gt 0 for all i , then th...

    Text Solution

    |

  5. If log2,log(2^x-1)a n dlog2log(2^x+3) are in A.P., write the value of ...

    Text Solution

    |

  6. If 1 , logy , x , logz , y , -15 logx z are in A.P. , then which is co...

    Text Solution

    |

  7. If x , y, z are in G.P. and a^x = b^y = c^z , then logb a* logb c is ...

    Text Solution

    |

  8. If log(2)(5.2^(x)+1),log(4)(2^(1-x)+1) and 1 are in A.P,then x equals

    Text Solution

    |

  9. I 1,log9(3^(1-x)+2), log3(4.3^x-1) are in A.P. then x equals (A) log34...

    Text Solution

    |

  10. If xgt1,ygt1,zgt1 are in G.P. then 1/(a+Inx), 1/(1+Iny), 1/(1+Inz) are...

    Text Solution

    |

  11. Let a1,a2 ,…. , a10 be in A.P. and h1,h2 …. h10 be in H.P. If a1=h1...

    Text Solution

    |

  12. Let S1 , S2 , …. Be squares such that for each n ge 1 the length of a...

    Text Solution

    |

  13. Let A1, G1, H1 denote the arithmetic, geometric and harmonic means, re...

    Text Solution

    |

  14. The arithmetic mean and geometric mean of two numbers are 10 and 18 re...

    Text Solution

    |

  15. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

    Text Solution

    |

  16. Let a1, a2, a3, ,a(100) be an arithmetic progression with a1=3a n dsp...

    Text Solution

    |

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

    Text Solution

    |

  18. Let a1,a2 ,…. , a10 be in A.P. and h1,h2 …. h10 be in H.P. If a1=h1...

    Text Solution

    |

  19. For a positive integer n , let a(n) = 1+ 1/2 + 1/3 +…+ 1/(2^(n)-1) ...

    Text Solution

    |

  20. What is the sum of the series 1+(1)/(2)+(1)/(4)+(1)/(8)+. . .?

    Text Solution

    |