Home
Class 12
MATHS
lim[x->1] ([sum[k=1]^100x^k]-100])/(...

`lim_[x->1] ([sum_[k=1]^100x^k]-100])/(x-1)`

Text Solution

Verified by Experts

The correct Answer is:
5050
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    MOTION|Exercise EXERCISE-4|17 Videos
  • LIMIT

    MOTION|Exercise EXERCISE-2(LEVEL-2)|5 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    MOTION|Exercise Exercise -4 Level -II|7 Videos
  • MATRICES

    MOTION|Exercise Exercise - 4 (Level-II)|28 Videos

Similar Questions

Explore conceptually related problems

Evaluate lim_(x to 1) sum_(k=1)^(100) x^(k) - 100)/(x-1).

Evaluate the limit: lim_(x rarr1)(sum_(k=1)^(oo0)x^(k)-100)/(x-1)

lim_ (x rarr1) ([sum_ (k = 1) ^ (100) x ^ (k)] - 100] ()) / (x-1)

lim_ (x rarr1) ((sum_ (k = 1) ^ (200) x ^ (K)) - 200) / (x-1)

k=lim_(xtooo)[(sum_(k=1)^(1000)(x+k)^(m))/(x^(m)+10^(1000))] (mgt101) is -

The coefficient of x^(50) in the expansion sum_(k=0)^(100)""^(100)C_(k)( x-2)^(100-k)3^(k) is also equal to :

(lim)_(x->0)([100 x/(sin^(-1)x)]+[100(tan^(-1)x)/x])=

MOTION-LIMIT-EXERCISE-3
  1. underset( x rarr oo) ("Lim") ((cos h ( pi //x))/(cos( pi//x)))^(x^(2))

    Text Solution

    |

  2. Evaluate lim(x->1)(root13 x- root 7 x)/(root5 x- root3 x)

    Text Solution

    |

  3. lim[x->1] ([sum[k=1]^100x^k]-100])/(x-1)

    Text Solution

    |

  4. lim(x ->oo)x^(2)(sqrt((x+2)/(x))-root(3)((x+3)/(x))) equals

    Text Solution

    |

  5. A circular are of radius 1 subtends an angle of x radians 0 < x < pi/2...

    Text Solution

    |

  6. A circular are of radius 1 subtends an angle of x radians 0 < x < pi/2...

    Text Solution

    |

  7. A circular are of radius 1 subtends an angle of x radians 0 < x < pi/2...

    Text Solution

    |

  8. At the end points A,B of the fixed segment of length L, lines are draw...

    Text Solution

    |

  9. At the endpoint and midpoint of a circular are AB, tangent lines are ...

    Text Solution

    |

  10. lim(x->0) [ ln(1+sin^2x) cot ln^2(1+x)]

    Text Solution

    |

  11. lim(x->oo)(a(2x^3-x^2)+b(x^3+5x^2-1)-c(3x^3+x^2))/(2(5x^4-x)-b x^4+c(4...

    Text Solution

    |

  12. find a&b if lim(x->oo) ((x^2+1)/(x+1)-ax-b)=0

    Text Solution

    |

  13. lim(x rarr oo) (sqrt(x^2-x+1)-a x-b)=0, then a+b=

    Text Solution

    |

  14. lim(x->0)[lim(x->oo)(e x p(xln(1+(a y)/x))-e x p(x In(1+(b y)/x)))/y]

    Text Solution

    |

  15. underset( x rarr 1) ( "Lim") ( tan "" ( pi x)/( 4))^(tan""( pix)/( 2))

    Text Solution

    |

  16. Let f(x)=(sin^-1(1-{x})*cos^-1(1-{x}))/(sqrt(2{x})(1-{x})), then find ...

    Text Solution

    |

  17. evaluate lim(x->a)1/((a^2-x^2)^2)((a^2+x^2)/(a x)-2sin((api)/2)sin((pi...

    Text Solution

    |

  18. Let x0=2(cos)pi/6and xn=sqrt(2+x(n-1)).n=1,2,3,....... find Lim(n->oo)...

    Text Solution

    |

  19. lim(x rarr 0)[ln(1+x)^(1+x)/(x^2)-1/x]

    Text Solution

    |

  20. f(x) is the function such that underset( x rarr 0 ) ("Lim") (f(x))/( x...

    Text Solution

    |