Home
Class 11
MATHS
Prove that (25)^(n+1)-24n+5735 is divisi...

Prove that `(25)^(n+1)-24n+5735` is divisible by `(24)^2` for all `n=1,2,...`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

Similar Questions

Explore conceptually related problems

Prove that 2.7^(n)+ 3.5^(n)-5 is divisible by 24 for all n in N

Prove that (n !)! is divisible by (n !)^((n-1)!)

Using the principle of mathematical induction. Prove that (x^(n)-y^(n)) is divisible by (x-y) for all n in N .

Prove that AA n,14^n-13n-1 is divisible by 13. (n in N)

Prove by induction that n(n+1)(2n+1) is divisible by 6 for all ninNN .

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all n in N

n(gt1) is a positive integer . Show that 14^(n)-13n-1 is divisible by 13 for all n .

Using principle of mathematical induction, prove that 7^(4^(n)) -1 is divisible by 2^(2n+3) for any natural number n.

By the principle of mathematical induction prove that (5^(2n)-1) is always divisible by 24 for all positive integral values of n.

Using mathematical induction to show that p^(n+1) +(p+1)^(2n-1) is divisible by p^2+p+1 for all n in N

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. The coefficient of three consecutive terms in the expansion of (1+x)^n...

    Text Solution

    |

  2. The sum of G. P 3, 6, 12,... 1536.

    Text Solution

    |

  3. Prove that (25)^(n+1)-24n+5735 is divisible by (24)^2 for all n=1,2,.....

    Text Solution

    |

  4. The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a).(...

    Text Solution

    |

  5. Find the coefficient of x^5 in the expansion of (1+x)^21+(1+x)^22+...+...

    Text Solution

    |

  6. If x^m occurs in the expansion of (x+(1/x^2))^(2n) then the coefficien...

    Text Solution

    |

  7. If the coefficients of 5^(th), 6^(th) and 7^(th) terms in the expansio...

    Text Solution

    |

  8. If (1+2x+x^(2))^(n) = underset(r=0)overset(2n)suma(r)x^(r), then a(r) ...

    Text Solution

    |

  9. In the expansion of (x^3-1/(x^2))^n ,n in N , if the sum of the coeff...

    Text Solution

    |

  10. If the coefficients of rth and (r+1)t h terms in the expansion of (3+7...

    Text Solution

    |

  11. In the expansion of (1+3x+2x^(2))^(6), find the coefficient of x^(11).

    Text Solution

    |

  12. If .^(n-1)Cr=(k^2-3)^nC(r+1), then k belongs to (a) (-oo,-2] (b) [2,...

    Text Solution

    |

  13. Prove that (3!)/(2(n+3))=sum(r=0)^n(-1)^r((n Cr)/((r+3)C3))

    Text Solution

    |

  14. Find the 5th term of the GP. 5/2, 1, .....

    Text Solution

    |

  15. The expression (x+((x^3-1)^(1/2))/2)^5+""(x-((x^3-1)^(1/2))/2)^5 is a ...

    Text Solution

    |

  16. Find ((dy) /dx) of sin(cosx) is

    Text Solution

    |

  17. In the binomial expansion of (a-b)^n,ngeq5, the sum of the 5th and 6t...

    Text Solution

    |

  18. Coefficient of x^11 in the expansion of (1+x^2)^4(1+x^3)^7(1+x^4)^12 i...

    Text Solution

    |

  19. Give the integers rgt1 , ngt2 and c0-efficients of (3r)^th and (r+2)^(...

    Text Solution

    |

  20. Find the coefficient of x^4 in the expansion of (x//2-3//x^2)^(10)dot

    Text Solution

    |