Home
Class 12
MATHS
Let alpha=sum(k=0)^(n)(((""^(n)C(k))^(2)...

Let `alpha=sum_(k=0)^(n)(((""^(n)C_(k))^(2))/(k+1))` and `beta=sum_(k=0)^(n-1)((""^(n)C_(k)^(n)C_(k+1))/(k+2))` .If `5 alpha=6 beta` ,then "n" equals________.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2024

    JEE MAINS PREVIOUS YEAR|Exercise Questions|18 Videos
  • JEE MAINS

    JEE MAINS PREVIOUS YEAR|Exercise Physics|30 Videos

Similar Questions

Explore conceptually related problems

Find the sum sum_(k=0)^n ("^nC_k)/(k+1)

Let U_(n)=sum_(k=1)^(n)(n)/(n^(2)+k^(2)),S_(n)=sum_(k=0)^(n-1)(n)/(n^(2)+k^(2)) then

S_(n)=sum_(k=1)^(n)(k^(2)+n^(2))/(n^(3)) and T_(n)=sum_(k=0)^(n-1)(k^(2)+n^(2))/(n^(3)),n in N then

The value of sum_(r=1)^(n+1)(sum_(k=1)^(n)C(k,r-1))=

If for n in N,sum_(k=0)^(2n)(-1)^(k)(2nC_(k))^(2)=A, then find the value of sum_(k=0)^(2n)(-1)^(k)(k-2n)(2nC_(k))^(2)

Let S_(n)=sum_(k=1)^(n) (n)/(n^(2)+nk+k^(2)) and T_(n)=sum_(k=0)^(n-1)(n)/(n^(2)+nk+k^(2)) for n= 1,2,3..., then

Given S_(n)=sum_(k=1)^(n)(k)/((2n-2k+1)(2n-k+1)) and T_(n)=sum_(k=1)^(n)(1)/(k) then (T_(n))/(S_(n)) is equal to

sum_(i=0)^(n)sum_(j=0)^(n)sum_(k=0)^(n)((n),(i))((n),(j))((n),(k)),((n),(r))=""^(n)C_(r) :

JEE MAINS PREVIOUS YEAR-JEE MAIN 2024 ACTUAL PAPER-Question
  1. The area of the region enclosed by the parabola (y-2)^(2)=x-1 ,the lin...

    Text Solution

    |

  2. The number of symmetric relations defined on the set {1,2,3,4} which a...

    Text Solution

    |

  3. Let alpha=sum(k=0)^(n)(((""^(n)C(k))^(2))/(k+1)) and beta=sum(k=0)^(n-...

    Text Solution

    |

  4. In an examination of Mathematics paper,there are "20" questions of equ...

    Text Solution

    |

  5. If one of the diameters of the circle x^(2)+y^(2)-10x+4y+13=0 is a cho...

    Text Solution

    |

  6. The distance of the point Q(0,2,-2) form the line passing through the ...

    Text Solution

    |

  7. lim(x rarr0)(e^(2|sin x|)-2|sin x|-1)/(x^(2))

    Text Solution

    |

  8. Let "a" be the sum of all coefficients in the expansion of (1-2x+2x^(2...

    Text Solution

    |

  9. The solution curve of the differential equation y(dx)/(dy)=x(log(e)x-l...

    Text Solution

    |

  10. Let vec a=3 hat i+hat j-2 hat k,vec b=4 hat i+hat j+7 hat k and vec c=...

    Text Solution

    |

  11. Three rotten apples are accidently mixed with fifteen good apples. Ass...

    Text Solution

    |

  12. The area of the region {(x,y):y^(2)le4x,x<4,(xy(x-1)(x-2))/((x-3)(x-4)...

    Text Solution

    |

  13. Let y=y(x) be the solution of the differential equation (dy)/(dx)=((ta...

    Text Solution

    |

  14. For 0 lt c lt b lt a ,let (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 and alpha...

    Text Solution

    |

  15. Let "g(x)" be a linear funchion and f(x)={[g(x),,xle0],[((1+x)/(2+x))^...

    Text Solution

    |

  16. Let sin^(-1)alpha+sin^(-1)beta+sin^(-1)gamma=pi and alpha, beta, gamma...

    Text Solution

    |

  17. Let "S" be the set of postive integral values of "a" for which (ax^(2)...

    Text Solution

    |

  18. If f(x)=(4x-3)/(6x-4),xne2/3,g:R-{2/3}toR-{2/3},g(x)=fof(x) then value...

    Text Solution

    |

  19. Two marbles are drawn in succession from a box containing "10" red,"30...

    Text Solution

    |

  20. If f(x)=|[x^(3),2x^(2)+1,1+3x],[3x^(2)+2,2x,x^(3)+6],[x^(3)-x,4,x^(2)-...

    Text Solution

    |