Home
Class 12
MATHS
If (x^(2)+x+1)/(1-x) = a(0) + a(1)x+a(2)...

If `(x^(2)+x+1)/(1-x) = a_(0) + a_(1)x+a_(2)x^(2)+"…."`, the b `sum_(r=1)^(50) a_(r)` equal to

A

148

B

146

C

149

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`((x^(2)+x+1)(1-x))/((1-x)^(2)) = (1-x^(3))(1-x)^(-2)`
`= (1-x^(3))(1+2x+3x^(2)+"....")`
Now, `a_(r) = (r+1)-(r-2)=3`
But `a_(1) = 2`
So, `underset(r=1)overset(50)suma_(r) = 2+49xx3=149`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.8|10 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

  • BINOMIAL THEORM

    CENGAGE|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

If (x^(2)+x+1)/(1-x)=a_(0)+a_(1)x+a_(2)x^(2)+..., then sum_(r=1)^(50)a_(r) is equal to 148 b.146 c.149 d.none of these

If (1+2x+3x^(2) )^(10) = a_(0) + a_(1) x + a_(2) x^(2) +…+a_(20) x^(20) , then

If e^(e^(x)) = a_(0) +a_(1)x +a_(2)x^(2)+... ,then find the value of a_ (0)

Let (x + 10)^(50) + (x - 10)^(50) = a_(0) + a_(1) x + a_(2)X^(2) + ….. + a_(50) x^(50) , for all x in R , then (a_(2))/(a_(0)) is equal to

If (1 + x+ 2x^(2))^(20) = a_(0) + a_(1) x + a_(2) x^(2) + …+ a_(40) x^(40) . The value of a_(0) + a_(2) + a_(4) + …+ a_(38) is

If (1 + x+ 2x^(2))^(20) = a_(0) + a_(1) x + a_(2) x^(2) + …+ a_(40) x^(40) . The value of (a_(39))/(a_(40)) , is

CENGAGE-BINOMIAL THEOREM-Exercise (Single)
  1. The value of sum(r=0)^(20)(-1)^(r )(""^(50)C(r))/(r+2) is equal to

    Text Solution

    |

  2. If (1+x^(2))^(n) =sum(r=0)^(n) a(r)x^(r )= (1+x+x^(2)+x^(3))^(100). If...

    Text Solution

    |

  3. sum(r=0)^(300) a(r)x^(r)=(1+x+x^(2)+x^(3))^(100). if a=sum(r=0)^(300)a...

    Text Solution

    |

  4. The value of sum(r=0)^(20) r(20-r)(""^(20)C(r))^(2) is equal to

    Text Solution

    |

  5. If f(x) = .^(40)C(1).x(1-x)^(39) + 2..^(40)C(2)x^(2)(1-x)^(38)+3..^(40...

    Text Solution

    |

  6. If a(n) = sum(r=0)^(n) (1)/(""^(n)C(r)), then the value of (sumsum)(0l...

    Text Solution

    |

  7. In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be 4...

    Text Solution

    |

  8. The sum of 1+n(1-1/x)+(n(n+1))/(2!)(1-1/x)^2+oo will be x^n b. x^(-n) ...

    Text Solution

    |

  9. sum(k=1)^(oo) k(1-1/n)^(k-1) =

    Text Solution

    |

  10. Find the coefficient of x in the expansion of [sqrt(1+x^2) - x]^-1 in...

    Text Solution

    |

  11. 1+1/3x+(1xx4)/(3xx6)x^2+(1xx4xx7)/(3xx6xx9)x^3+ is equal to x b. (1+x)...

    Text Solution

    |

  12. 1+1/4 + (1xx3)/(4xx8) + (1xx3xx5)/(4xx8xx12) x^(3) + "….." is equal to

    Text Solution

    |

  13. If |x|<1,t h e n1+n((2x)/(1+x))+(n(n+1))/(2!)((2x)/(1+x))^2+ is equal ...

    Text Solution

    |

  14. Find the coefficient of x^5 in (1+2x+3x^2...........)^(-3/2)

    Text Solution

    |

  15. If |x|<1, then the coefficient of x^n in expansion of (1+x+x^2+x^3+)^2...

    Text Solution

    |

  16. If x is positive, the first negative term in the expansion of (1+x)^(2...

    Text Solution

    |

  17. If x is so small that x^3 and higher powers of x may be neglectd, then...

    Text Solution

    |

  18. If the expansion in power of x of the function (1)/(( 1 - ax)(1 - b...

    Text Solution

    |

  19. If (x^(2)+x+1)/(1-x) = a(0) + a(1)x+a(2)x^(2)+"….", the b sum(r=1)^(50...

    Text Solution

    |

  20. If (1-x)^(-n)=a0+a1x+a2x^2++ar x^r+ ,t h e na0+a1+a2++ar is equal to (...

    Text Solution

    |