Home
Class 11
MATHS
If sum(r=1)^n r(r+1)(2r+3)=a n^4+b n^3+c...

If `sum_(r=1)^n r(r+1)(2r+3)=a n^4+b n^3+c n^2+d n+e ,` then (a) `a-b=d-c` (b) `e=0` (c) `a , b-2//3, c-1` are in A.P. (d) `(b+d)//a` is an integer

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If sum_(r=0)^(n) (pr+2).""^(n)C_(r)=(25)(64) where n, p in N , then (a) p=3 (b) p=4 (c) n=7 (d) n=6

If sum_(r=1)^(n) r(r+1) = ((n+a)(n+b)(n+c))/(3) , where a gt b gt c , then

If sum _(r=1)^n (r^2+1)r! =200xx201! Then n= (A) 200 (B) 201 (C) 199 (D) none of these

If sum_(r=0)^(n)((r+2)/(r+1)).^n C_r=(2^8-1)/6 , then n is (A) 8 (B) 4 (C) 6 (D) 5

If sum_(r=1)^n t_r= (n(n+1)(n+2))/3 then sum _(r=1)^oo 1/t_r= (A) -1 (B) 1 (C) 0 (D) none of these

Find sum of sum_(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^(n-1)+1 (d) None of these

If sum_(r=1)^(n)r(r+1)+sum_(r=1)^(n)(r+1)(r+2)=(n(an^(2)+bn+c))/(3),(a,b,cinN) then (A) a + b + c = 24 (B) 2a + b - c = 0 (C) a - b + c= 6 (D) ab + bc + ca = 11

If 1/(b-a)+1/(b-c)=1/a+1/c , then (A). a ,b ,a n dc are in H.P. (B). a ,b ,a n dc are in A.P. (C). b=a+c (D). 3a=b+c

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

If ^n P_r=960 and ^n C_r=40 ,then, r= a. 3 b. 4 c. 5 d. 6

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. After striking the floor, a certain ball rebounds (4/5)th of height ...

    Text Solution

    |

  2. If S denotes the sum to infinity and Sn the sum of n terms of the seri...

    Text Solution

    |

  3. The first term of an infinite geometric series is 21. The second term ...

    Text Solution

    |

  4. Given that x+y+z=15 when a ,x ,y ,z ,b are in A.P. and 1/x+1/y+1/z=5/3...

    Text Solution

    |

  5. Let a1,a2,a3…… ,an be in G.P such that 3a1+7a2 +3a3-4a5=0 Then common...

    Text Solution

    |

  6. The consecutive digits of a three digit number are in G.P. If middle ...

    Text Solution

    |

  7. If Sn=1^2-2^2+3^2-4^2+5^2-6^2+ ,t h e n S(40)=-820 b. S(2n)> S(2n+2) ...

    Text Solution

    |

  8. If sum(r=1)^n r(r+1)(2r+3)=a n^4+b n^3+c n^2+d n+e , then (a) a-b=d-c ...

    Text Solution

    |

  9. Find the sum off the terms of an infinite decreasing G.P. in which all...

    Text Solution

    |

  10. If a,x,b are in A.P.,a,y,b are in G.P. and a,z,b are in H.P. such that...

    Text Solution

    |

  11. If a,b, and c are in G.P then a+b,2b and b+ c are in

    Text Solution

    |

  12. If in a progression a1, a2, a3,.......... e tc dot,(ar-a(r+1)) bears...

    Text Solution

    |

  13. a ,b ,c x in R^+ such that a ,b ,a n dc are in A.P. and b ,ca n dd ar...

    Text Solution

    |

  14. Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equ...

    Text Solution

    |

  15. Let a in (0,1] satisfies the equation a^(2008)-2a+1=0 and S=1+a+a^2+.....

    Text Solution

    |

  16. If a ,b and c are in A.P. and b-a ,c-b and a are in G.P., then a : b :...

    Text Solution

    |

  17. If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a ...

    Text Solution

    |

  18. The sum of three numbers in G.P. is 14. If one is added to the first ...

    Text Solution

    |

  19. If x ,2x+2 and 3x+3 are the first three terms of a G.P., then the four...

    Text Solution

    |

  20. The harmonic mean of two numbers is 4, their arithmetic mean A and geo...

    Text Solution

    |