Home
Class 12
MATHS
If (1)/(log(2)a)+(1)/(log(4)a)+(1)/(log(...

If `(1)/(log_(2)a)+(1)/(log_(4)a)+(1)/(log_(8)a)+(1)/(log_(16)a)+….+`
`(1)/(log_(2^(n))a) = (n(n+1))/(k)` then k `log_(a)2` is equal to

A

2

B

3

C

1

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
`If (1)/(log_(2)a)+(1)/(log_(4)a)+(1)/(log_(8)a)` …………
Given
`log_(a)2+log_(a)2^(2)+……+log_(a)2^(n) = (n(n+1))/(k)`
`implies (1+2+3+…….+n)log_(a)2 = (n(n+1))/(k)`
`implies (n(n+1))/(2). Log_(a)2 = (n(n+1))/(k)`
`implies k. log_(a)2 = 2`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE|Exercise PART : 1MATHEMATICS SEC - 1|1 Videos

  • TEST PAPERS

    RESONANCE|Exercise PART : 1MATHEMATICS|9 Videos

  • TEST PAPER

    RESONANCE|Exercise CHEMISTRY|37 Videos

  • TEST SERIES

    RESONANCE|Exercise MATHEMATICS|131 Videos

Similar Questions

Explore conceptually related problems

If (1)/("log"_(2)a) + (1)/("log"_(4)a) + (1)/("log"_(8)a) + (1)/("log"_(16)a) + …. + (1)/("log"_(2^(n))a) = (n(n+1)/(lambda)) then lambda equals

(1)/(log_(2)N)+(1)/(log_(3)N)+(1)/(nog_(4)N)+...+(1)/(log_(2011)N)=(1)/(log_(2011)N)

(1)/(log_(2)(n))+(1)/(log_(3)(n))+(1)/(log_(4)(n))+....+(1)/(log_(43)(n))

(1)/(log_(2)(n))+(1)/(log_(3)(n))+(1)/(log_(4)(n))+....+(1)/(log_(43)(n))

(1)/("log"_(2)n) + (1)/("log"_(3)n) + (1)/("log"_(4)n) + … + (1)/("log"_(43)n)=

Show that: (1)/(log_(2)n)+(1)/(log_(3)n)+(1)/(log_(4)n)+...+(1)/(log_(43)n)=(1)/(log_(43!)n)

RESONANCE-TEST PAPERS-MATHEMATICS
  1. If (1)/(log(2)a)+(1)/(log(4)a)+(1)/(log(8)a)+(1)/(log(16)a)+….+ (1)/...

    Text Solution

    |

  2. The least positive integral value of 'k' for which there exists at lea...

    Text Solution

    |

  3. The locus of the midpoint of a chord of the circle x^2+y^2=4 which sub...

    Text Solution

    |

  4. If f(x)=x+tanx and g(x) is inverse of f(x) then g^(')(x) is equal to

    Text Solution

    |

  5. Tangents PA and PB are drawn to parabola y^(2)=4x from any arbitrary p...

    Text Solution

    |

  6. If lim(nrarroo) (n.2^(n))/(n(3x-4)^(n)+n.2^(n+1)+2^(n))=1/2 where "n" ...

    Text Solution

    |

  7. Eccentricity of ellipse 2(x-y+1)^(2)+3(x+y+2)^(2)=5 is

    Text Solution

    |

  8. If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y. Then which ...

    Text Solution

    |

  9. If f:RrarrR is a continuous function satisfying f(0)=1 and f(2x)-f(x)=...

    Text Solution

    |

  10. tan^(-1)(sinx)=sin^(-1)(tanx) holds true for

    Text Solution

    |

  11. is The function f(x)=(x^2-1)|x^2-3x+2|+cos(|x|) is differentiable not ...

    Text Solution

    |

  12. Consider parabola P(1)-=y=x^(2) and P(2)-=y^(2)=-8x and the line L-=lx...

    Text Solution

    |

  13. If the normals at (x(i),y(i)) i=1,2,3,4 to the rectangular hyperbola x...

    Text Solution

    |

  14. Let f(x)=x^(3)-x^(2)+x+1 and g(x)={("max "f(t) 0letlex 0lexle1),(3-x 1...

    Text Solution

    |

  15. The value(s) of x satisfying tan^(-1)(x+3)-tan^(-1)(x-3)=sin^(-1)(3/5)...

    Text Solution

    |

  16. For an ellipse having major and minor axis along x and y axes respecti...

    Text Solution

    |

  17. If f:[0,1]rarrR is defined as f(x)={(x^(3)(1-x)"sin"1/(x^(2)) 0ltxle1)...

    Text Solution

    |

  18. If f(x)=root (3)(8x^(3)+mx^(2))-nx such that lim(xrarroo)f(x)=1 then

    Text Solution

    |

  19. For the curve y=4x^3-2x^5,find all the points at which the tangent pa...

    Text Solution

    |

  20. Minimum value of (sin^(-1)x)^(2)+(cos^(-1)x)^(2) is greater than

    Text Solution

    |

  21. If y+a=m(1)(x+3a),y+a=m(2)(x+3a) are two tangents to the parabola y^(2...

    Text Solution

    |