Home
Class 12
MATHS
For each positive integer n , let f(n+1)...

For each positive integer `n ,` let `f(n+1)=n(-1)^(n+1)-2f(n)` and `f(1)=(2010)dot` Then `sum_(k=1)^(2009)f(K)` is equal to 335 (b) 336 (c) 331 (d) 333

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

For each positive integer n, let f(n+1)=n(-1)^(n+1)-2f(n) and f(1)=(2010)* Then sum_(k=1)^(2009)f(K) is equal to 335(b)336(c)331(d)333

If f(n) = [(1)/(3)+(n)/(100)] , where [.] denotes G.I.F then sum_(n=1)^(200)f(n) is equal to

Let sum_(r=1)^(n) r^(6)=f(n)," then "sum_(n=1)^(n) (2r-1)^(6) is equal to

For any positive n, let f(n)=(4n+sqrt(4n^(2)-1))/(sqrt(2n+1)+sqrt(2n-1)) . Then ((Sigma_(k=1)^(40)f(k))/(100)) is equal to

Let sum_(r=1)^(n)r^(4)=f(n)," then " sum_(r=1)^(n) (2r-1)^(4) is equal to

Let sum_(r=1)^(n)(r^(4))=f(n). Then sum_(r=1)^(n)(2r-1)^(4) is equal to :

If f(n+1)=(2f(n)+1)/(2) for n=1, 2, 3……….. and f(1)=2 , then (f(101))/(10) is equal to

f(1)=1 and f(n)=2sum_(r=1)^(n-1)f(r). Then sum_(n=1)^(m)f(n) is equal to (A)3^(m)-1(B)3^(m)(C)3^(m-1) (D)none of these

For which positive integers n is the ratio (sum_(k=1)^(n)k^(2))/(sum_(k=1)^(n)k) an integer?

For which positive integers n is the ratio, (sum+(k=1)^(n) k^(2))/(sum_(k=1)^(n) k) an integer ?

RESONANCE DPP-JEE MAINS-All Questions
  1. If roots of x^3+bx^2+cx+d=0 are (A) in A.P. then 2b^3-9bc+27d=0 (B) ...

    Text Solution

    |

  2. Solve the equation 2sin^(-1)x=tan^(-1)((2xsqrt(1-x^2))/(1-2x^2))

    Text Solution

    |

  3. For each positive integer n , let f(n+1)=n(-1)^(n+1)-2f(n) and f(1)=(2...

    Text Solution

    |

  4. If y(x) is the solution of the differential equation (dy)/(dx)=-2x(y-1...

    Text Solution

    |

  5. If alpha and beta are the roots of the quadratic equation x^(2) - 4...

    Text Solution

    |

  6. Let f(x) =x^2+ ax + b cos x, a being an integer and b is a real numbe...

    Text Solution

    |

  7. Solve for x :5^(logx)+5x^(log5)=3(a >0); where base oflog\ is a

    Text Solution

    |

  8. A parabola is drawn whose focus is one of the foci of the ellipse x^2...

    Text Solution

    |

  9. Let C1 and C2 are circles defined by x^2+y^2 -20x+64=0 and x^2+y^2+...

    Text Solution

    |

  10. The number solution of the equation sgn(x^2)=|x-2| is 1 (b) 0 (c) 2...

    Text Solution

    |

  11. If alpha,beta are the roots of the equation, x^2-2x+3=0, find the e...

    Text Solution

    |

  12. The function f(x)={ 1-2x+3x^2-4x^3; x!=-1, 1; x=-1} discuss the co...

    Text Solution

    |

  13. Let f(x) be a differentiable function such that f(x)=x^2 +int0^x e^-t ...

    Text Solution

    |

  14. If (x1, y1)&(x2, y2) are the solutions of the equaltions, (log)(225)(x...

    Text Solution

    |

  15. Investigate for the maxima and minima of the function f(x)=int1^x[2(t...

    Text Solution

    |

  16. The solution of the equation 7^(logx)-5^(logx+1)=3. 5^(logx-1)-13. 7^(...

    Text Solution

    |

  17. int0^1(e^x dx)/(1+e^x)

    Text Solution

    |

  18. Find the equation of the curve in which the perpendicular from the ori...

    Text Solution

    |

  19. If the difference of the roots of the equation, x^2+p x+q=0 be unity, ...

    Text Solution

    |

  20. If two events Aa n dB are such that P(A^c)=0. 3 ,P(B)=0. 4 ,a n dP...

    Text Solution

    |