Home
Class 11
MATHS
If f(n)=sum(r=1)^n[r(n ^(n-1)C(r-1)-r^C(...

If `f(n)=sum_(r=1)^n[r(n ^(n-1)C_(r-1)-r`^C_(r-1))+(2r+1)`^nC_r]`

A

`f(n)=n^2-1`

B

`f(n)=(n+1)^2-1`

C

`sum_(n=1)^10 f(n)=495`

D

`sum_(n=1)^10 f(n)=374`

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    PATHFINDER|Exercise QUESTION BANK |266 Videos

  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

.^(n-1)C_(r)+^(n-1)C_(r-1)=

Find the sum sum_(r=1)^n r^n (^nC_r)/(^nC_(r-1)) .

Find the sum of sum_(r=1)^n r* (nC_r)/(nC_(r-1)

msum_(r=1)^n1/nsqrt((n+r)/(n-r))

show that ^nC_r+ ^(n-1)C_(r-1)+ ^(n-1)C_(r-2)= ^(n+1)C_r

If sum_(r=0)^(n){("^(n)C_(r-1))/('^(n)C_(r )+^(n)C_(r-1))}^(3)=(25)/(24) , then n is equal to (a) 3 (b) 4 (c) 5 (d) 6

Show that , (.^(n)C_(r)+^(n)C_(r-1))/(.^(n)C_(r-1)+^(n)C_(r-2))=(.^(n+1)p_(r))/(r.^(n+1)p_(r-1))

The result of ^(n-1)C_r+^(n-1)C_(r-1)=

If "^(n)C_(0)-^(n)C_(1)+^(n)C_(2)-^(n)C_(3)+...+(-1)^(r )*^(n)C_(r )=28 , then n is equal to ……

The value of sum_(r=1)^(n)(-1)^(r-1)((r )/(r+1))*^(n)C_(r ) is (a) 1/(n+1) (b) 1/n (c) 1/(n-1) (d) 0

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. Number of values of r satisfying the equation ,^69C(3r-1) -^(69)C(r^2)...

    Text Solution

    |

  2. In the expansion of (x+(a/x^2))^n, (ane0) if term independent of x doe...

    Text Solution

    |

  3. If f(n)=sum(r=1)^n[r(n ^(n-1)C(r-1)-r^C(r-1))+(2r+1)^nCr]

    Text Solution

    |

  4. The value of ,^nC0 + ^(n+1)C1 +^(n+2)C2+……+^(n+k)Ck is equal to

    Text Solution

    |

  5. If the expansion of (x+(alpha/x))^n and (x+(beta/x^2))^n in powers of ...

    Text Solution

    |

  6. The coefficient of the middle term in the expansion of (1+x)^(2n) is

    Text Solution

    |

  7. If the term independent of x in the expansion of (sqrtx+(k/x^2))^10 is...

    Text Solution

    |

  8. If n is a positive integer then in the trinomial expansion of (x^2+2x+...

    Text Solution

    |

  9. Which of the following will not be true?

    Text Solution

    |

  10. Consider following two infinite series in real r and 0 C=1+rcostheta...

    Text Solution

    |

  11. Consider following two infinite series in real r and 0 C=1+rcostheta...

    Text Solution

    |

  12. First three terms in the expansion of (x+a)^n are respectively 128, 22...

    Text Solution

    |

  13. The sum of even terms in the expansion of (x+a)^n is

    Text Solution

    |

  14. Match List - I with List-II

    Text Solution

    |

  15. Match List-I with List-II

    Text Solution

    |

  16. If the second term of the expansion [a^(1/13)+(a/sqrt(a^(-1))] is 14a^...

    Text Solution

    |

  17. (1+x)(1+x+x^2)(1+x+x^2+x^3)…….(1+x+x^2+…….+x^(100)) when written in th...

    Text Solution

    |

  18. The value of {3^(2003)/28}=a/b where {} denotes the fractional part th...

    Text Solution

    |

  19. The coefficient of x^4 in the expansion of (1+x+x^2+x^3)^11 is lamda ....

    Text Solution

    |

  20. The fractional part of the sum of all the rational terms in the expans...

    Text Solution

    |