Home
Class 12
MATHS
Sum of the series sum0^10 (-1)^r 10Cr (1...

Sum of the series `sum_0^10 (-1)^r 10C_r (1/3^r+8^r/3^(2r)) is `

A

`(2^(10)+1)/(3^(20))`

B

`((2)/(3))^(10) - ((1)/(9))^(10)`

C

`(3^(10)-1)/(3^(20))`

D

`(6^(10)+1)/(3^(20))`

Text Solution

Verified by Experts

The correct Answer is:
D
Sum of the series…………….
`sum(-1)^(r-10)C_(r )((1)/(3))^(r )+sum(-1)^(r-10)C_(r )((8)/(9))^(r )`
`= (1-(1)/(3))^(n)+(1-(8)/(9))^(n)=((2)/(3))^(n)+((1)/(9))^(n)= (6^(n)+1)/(3^(2n))`
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

Let C_r = ""^(15)C_(r), 0ler <=15 . Sum of the series S=sum_(r=1)^(15)r(C_(r))/(C_(r-1)) is

Sum of the series sum_(r=1)^(n)(r^(2)+1)r!, is

Sum of the series sum_(r=1)^(n) (r^(2)+1)r! is

Sum of the series sum_(r=0)^(n)(-1)^(r)^^nC_(r)[i^(5r)+i^(6r)+i^(7r)+i^(8r)] is

find the sum of the series sum_(r=0)^(n)(-1)^(r)*^(n)C_(r)[(1)/(2^(r))+(3^(r))/(2^(2r))+(7^(r))/(2^(3r))+(15^(r))/(2^(4r))... up to m terms ]

Find the sum of the series sum_(r=1)^(n)r xx r!

The sum of the series sum_(r=1)^(n)(-1)^(r-1)*nC_(r)(a-r) is equal to :

RESONANCE-TEST PAPERS-MATHEMATICS
  1. Sum of the series sum0^10 (-1)^r 10Cr (1/3^r+8^r/3^(2r)) is

    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

    |