Home
Class 12
MATHS
Let "Delta"r=|r x(n(n+1))/2 2r-1y n^2 3r...

Let `"Delta"_r=|r x(n(n+1))/2 2r-1y n^2 3r-2z(n(3n-1))/2|` . Show that `sum_(r=1)^n"Delta"_r=0` .

Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos
  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos

Similar Questions

Explore conceptually related problems

Let Delta_r=|[r , x , (n(n+1))/2] , [2r-1 , y , n^2] , [3r-2 , z , (n(3n-1))/2]|dot Show that sum_(r=1)^n Delta_r=0

Let "Delta"_r=|r-1n6(r-1)^2 2n^2 4n-2(r-1)^2 3n^3 3n^2-3n|dot Show that sum_(r=1)^n"Delta"_r is contant.

If Dr=|[r,n+1,1],[r^2,2n-1,(2n+1)/3],[r^3,3n+2,(n(n+1))/2]|, show that sum_(r=1)^n Dr=0

If D_r=|2^(r-1)2(3^(r-1))4(5^(r-1))x y z2^n-1 3^n-1 5^n-1| then prove that sum_(r=1)^n D_r=0.

Suppose n epsilon N and for 1lerlen Let Deltar=|(3r-2,2020,3n-1),(2r-1,2025,2n),(r,2029,n+1)| then 1/(3n) sum_(r=1)^(n)(Delta_(r)+6) is equal to __________

If Delta_r=|[2^(r-1)2 , 3^(r-1) , 4. 5^(r-1)] , [x , y , z] , [2^n-1 , 3^n-1 , 5^n-1]|dot Show that sum_(r=1)^n Delta_r=Con s t a n t

If D_(r) = |(r,1,(n(n +1))/(2)),(2r -1,4,n^(2)),(2^(r -1),5,2^(n) -1)| , then the value of sum_(r=1)^(n) D_(r) , is

" Let " Delta_(r)=|{:(r-1,,n,,6),((r-1)^(2),,2n^(2),,4n-2),((r-1)^(2),,3n^(3),,3n^(2)-3n):}|. " Show that " Sigma_(r=1)^(n) Delta_(r) is constant.

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Prove that: |b c-a^2c a-b^2a b-c^2c a-b^2a b-c^2b c-a^2a b-c^2b c-a^2c...

    Text Solution

    |

  2. f(x)=|(secx,cos x,sec^2x + cot x cosecx),(cos^2x,cos^2x,cosec^2 x),(1,...

    Text Solution

    |

  3. Let "Delta"r=|r x(n(n+1))/2 2r-1y n^2 3r-2z(n(3n-1))/2| . Show that su...

    Text Solution

    |

  4. If "Delta"r=|2^(r-1)2. 3^(r-1)4. 5^(r-1)x y z2^n-1 3^n-1 5^n-1|dot Sho...

    Text Solution

    |

  5. If m is a positive integer and Dr=|(2r-1,\ ^m Cr,1),(m^2-1, 2^m ,m+1...

    Text Solution

    |

  6. Without expanding evaluate the determinant "Delta"=|(1, 1, 1),(a, b,...

    Text Solution

    |

  7. Without expanding, show that "Delta"=|(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y...

    Text Solution

    |

  8. Prove that: |-2a a+b a+c b+a-2bb+cc+a c+b-2c|=4(a+b)(b+c)(c+a)

    Text Solution

    |

  9. Without expanding, show that the value of each of the following det...

    Text Solution

    |

  10. Prove: |(1,b+c ,b^2+c^2),( 1,c+a ,c^2+a^2),( 1,a+b ,a^2+b^2)|=(a-b)(b-...

    Text Solution

    |

  11. Prove: |(a, a+b, a+2b),( a+2b, a ,a+b ),(a+b, a+2b, a)|=9(a+b)b^2

    Text Solution

    |

  12. Prove: |(1,a, b c),(1,b ,c a),(1,c ,a b)|=|(1,a ,a^2),( 1,b,b^2),( 1,c...

    Text Solution

    |

  13. Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b...

    Text Solution

    |

  14. Prove: |(x+4,x,x),(x,x+4,x),(x,x,x+4)|=16(3x+4)

    Text Solution

    |

  15. Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|=

    Text Solution

    |

  16. Prove: |(a, b-c,c-b),( a-c, b, c-a),( a-b,b-a, c)|=(a+b-c)(b+c-a)(c+a-...

    Text Solution

    |

  17. Prove: |a^2+1a b a c a bb^2+1b cc a c b c^2+1|=1+a^2+b^2+c^2

    Text Solution

    |

  18. Prove: |1a a^2a^2 1a a a^2 1|=(a^3-1)^2

    Text Solution

    |

  19. Prove: |b+c a a b c+a b cc a+b|=4a b c

    Text Solution

    |

  20. Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

    Text Solution

    |