Home
Class 11
MATHS
By mathematical induction prove that, (n...

By mathematical induction prove that, `(n^(7))/(7)+(n^(5))/(5)+(2n^(3))/(3)-(n)/(105)` is an integer for all `ninNN`.

Text Solution

Verified by Experts

The correct Answer is:
`ninNN`.
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION

    CHHAYA PUBLICATION|Exercise Exercise|57 Videos

  • MATHEMATICAL INDUCTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams|20 Videos

  • HYPERBOLA

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMS|12 Videos

  • STRAIGHT LINE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Assertion-Reason Type)|2 Videos

Similar Questions

Explore conceptually related problems

If ninNN , then by princuple of mathematical induction prove that, (n^(11))/(11)+(n^(5))/(5)+(n^(3))/(3)+(62n)/(165) is an integer.

If ninNN , then by princuple of mathematical induction prove that, (1)/(5)n^(5)+(1)/(3)n^(3)+(1)/(15)*7n is an integer.

Show that (n^(5))/(5)+(n^(3))/(3)+(7n)/(15) is a natural number, for all n inN

By principle of mathematical induction,prove that 1^(3)+2^(3)+3^(3)+ . . .. +n^(3)=[(n(n+1))/(2)]^(2) for all ninNN

Using the principle of mathematical induction, prove that 1.3 + 2.3^(2) + 3.3^(2) + ... + n.3^(n) = ((2n-1)(3)^(n+1)+3)/(4) for all n in N .

By mathematical induction prove that, 1*2+2*2^(2)+3*2^(3)+ . . .+n*2^(n)=(n-1)*2^(n+1)+2,ninNN .

Using mathematical induction prove that (d)/(dx)(x^n)= nx^(n-1) for all positive integers n.

Prove by mathematical induction that, 2n+7lt(n+3)^(2) for all ninNN .

If ninNN , then by principle of mathematical induction prove that, .^(n)C_(0)+.^(n)C_(1)+.^(n)C_(2)+ . . .+.^(n)C_(n)=2^(n)(ninNN)

Using mathematical induction, prove that 1/5n^5+1/3n^3+7n/15 is a natural number where ninN .

CHHAYA PUBLICATION-MATHEMATICAL INDUCTION -Sample Questions for Competitive Exams
  1. By mathematical induction prove that, (n^(7))/(7)+(n^(5))/(5)+(2n^(3))...

    Text Solution

    |

  2. If for all ninNN and nge1, then (3^(2^(n))-1) is always divisible by

    Text Solution

    |

  3. If ninNN , both expression n(n+1)(n+2) and n(n+1)(n+5) are multiple of...

    Text Solution

    |

  4. The value of n for which n!gt2^(n) will true, are -

    Text Solution

    |

  5. If n is even then the expression n(n^(2)+20) is divisible by the numbe...

    Text Solution

    |

  6. If p inNN then the expression p^(n+1)+(p+1)^(2n-1) is divisible by the...

    Text Solution

    |

  7. 10^(n)+3*4^(2)+5 is always divisible by the number -

    Text Solution

    |

  8. 3^(2n) when divided by 8 leves the remainder-

    Text Solution

    |

  9. If n be a positive integer, then the digit in the unit's place of 3^(2...

    Text Solution

    |

  10. For a positive integer n,n(n+1)(2n+1) when divided by 6 leaves the rem...

    Text Solution

    |

  11. ninNN,(n+1)^(3)+(n+2)^(3)+(n+3)^(3) when divided by 9, then the remain...

    Text Solution

    |

  12. Match the entries given in left column with those given in right colum...

    Text Solution

    |

  13. Match the entries given in left column with those given in right colum...

    Text Solution

    |

  14. P(n):11^(n+2)+1^(2n+1) where n is a positive integer p(n) is divisib...

    Text Solution

    |

  15. P(n):11^(n+2)+1^(2n+1) where n is a positive integer If P(n) = 14642...

    Text Solution

    |

  16. P(n):11^(n+2)+1^(2n+1) where n is a positive integer If n=3, then th...

    Text Solution

    |

  17. If n be a positive integer and P(n):4^(5n)-5^(4n) P(n) is divisible ...

    Text Solution

    |

  18. If n be a positive integer and P(n):4^(5n)-5^(4n) If P(n) be negativ...

    Text Solution

    |

  19. If n be a positive integer and P(n):4^(5n)-5^(4n) When n=3 then the ...

    Text Solution

    |

  20. underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)...

    Text Solution

    |

  21. Statement - I : For every natural number ((n+4)!)/((n+1)!) is divisibl...

    Text Solution

    |