Home
Class 11
MATHS
If ninN,xgt-1 and (1+x)^(n)ge1+nx, then ...

If `ninN,xgt-1 `and `(1+x)^(n)ge1+nx`, then prove that `(1+x)^(n+1)ge1+(n+1)x`.

Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams|20 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

For ninN , prove that ((n+1)/2)^ngt n!

If n is a positive integer and U_(n) = (3 + sqrt5)^(n) + (3 - sqrt5)^(n) , then prove that U_(n + 1) = 6U_(n) - 4U_(n -1), n ge 2

If the first three terms in the expansion of (1+x)^(n) are in A .P . , prove that, n(n-1)x^(2)-4nx+2=0 .

Solve: (-1)/(|x|-2) ge 1 .

If y=((1+x)/(1-x))^(n) , prove that (1-x^(2))(d^(2)y)/(dx^(2))=2(n+x)(dy)/(dx).

Prove that lim_(xrarr0) ((1+x)^(n) - 1)/(x) = n .

If a_1. a_2 ....... a_n are positive and (n - 1) s = a_1 + a_2 +.....+a_n then prove that (a_1 + a_2 +....+a_n)^n ge (n^2 - n)^n (s - a_1) (s - a_2)........(s - a_n)

If x prop y+z , y propz+x and z prop x+y , and the constant of variation are 1,m,n respectively, then prove that, l/(l+1)+m/(m+1)+n/(n+1) = 1

If x > 0, y >0, z > 0 and x +y + z = 1 , prove that (1+x)(1+y)(1+z)ge 8(1-x) (1-y) (1-z)

Prove that the coefficents of x^(n) in the expansion of (1+x)^(2n) is twice the coefficent of x^(n) in the expansion of (1+x)^(2n-1) .

CHHAYA PUBLICATION-MATHEMATICAL INDUCTION -Exercise
  1. If [12^(n)+25^(n-1)] is divisible by 13, then show that [12^(n+1)+25^(...

    Text Solution

    |

  2. If [n^(3)+(n+1)^(3)+(n+2)^(3)] is also divisible by 9. then show that,...

    Text Solution

    |

  3. If ninN,xgt-1 and (1+x)^(n)ge1+nx, then prove that (1+x)^(n+1)ge1+(n+1...

    Text Solution

    |

  4. Let f(n)=n(n+1)(2n+1), if f(n) is always divisible ny 6 then prove tha...

    Text Solution

    |

  5. For all ninNN, prove by principle of mathematical induction that, 1+...

    Text Solution

    |

  6. For all ninNN, prove by principle of mathematical induction that, a+...

    Text Solution

    |

  7. For all ninNN, prove by principle of mathematical induction that, si...

    Text Solution

    |

  8. For all ninNN, prove by principle of mathematical induction that, si...

    Text Solution

    |

  9. For all ninNN, prove by principle of mathematical induction that, (c...

    Text Solution

    |

  10. For all ninNN, prove by principle of mathematical induction that, (1...

    Text Solution

    |

  11. For all ninNN, prove by principle of mathematical induction that, a+...

    Text Solution

    |

  12. For all ninNN, prove by principle of mathematical induction that, 1^...

    Text Solution

    |

  13. For all ninNN, prove by principle of mathematical induction that, 1*...

    Text Solution

    |

  14. For all ninNN, prove by principle of mathematical induction that, 2^...

    Text Solution

    |

  15. For all ninNN, prove by principle of mathematical induction that, (1...

    Text Solution

    |

  16. For all ninNN, prove by principle of mathematical induction that, (1...

    Text Solution

    |

  17. For all ninNN, prove by principle of mathematical induction that, (1...

    Text Solution

    |

  18. For all ninNN, prove by principle of mathematical induction that, 1+...

    Text Solution

    |

  19. For all ninNN, prove by principle of mathematical induction that, 1*...

    Text Solution

    |

  20. For all ninNN, prove by principle of mathematical induction that, 2^...

    Text Solution

    |