Home
Class 11
MATHS
Prove the following by using the Princip...

Prove the following by using the Principle of mathematical induction `AA n in N`
`(1-(1)/(2))(1-(1)/(3)) (1-(1)/(4))…….(1-(1)/(n+1))=(1)/(n+1)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • PRINCIPAL OF MATHEMATICAL INDUCTION

    CBSE COMPLEMENTARY MATERIAL|Exercise Very Short Answer Type Questions(M.C.Q)|3 Videos

  • PRACTICE PAPER-II

    CBSE COMPLEMENTARY MATERIAL|Exercise Section-D (Long Answer Type-I)|7 Videos

  • PROBABILITY

    CBSE COMPLEMENTARY MATERIAL|Exercise LONG ANSWER TYPE QUESTIONS|23 Videos

Similar Questions

Explore conceptually related problems

Prove the following by using the Principle of mathematical induction AA n in N 2^(n+1)>2n+1

Prove the following by using the principle of mathematical induction for all n in Nvdots(1+(1)/(1))(1+(1)/(2))(1+(1)/(3))...(1+(1)/(n))=(n+1)

Prove the following by using the Principle of mathematical induction AA n in N and n>1 1+(1)/(4)+(1)/(9)+…….+(1)/(n^(2))<2-(1)/(n)

Prove the following by using the Principle of mathematical induction AA n in N 2^(3n-1) is divisble by 7.

Prove the following by using the Principle of mathematical induction AA n in N (1+x)^nge1+nx, where, xge-1

Prove the following by the principle of mathematical inductiten: (1-(1)/(2^(2)))(1-(1)/(3^(2)))(1-(1)/(4^(2)))(1-(1)/(n^(2)))=(n+1)/(2n) or all natural numbers n>=2.

Prove the following by using the principle of mathematical induction for all n in Nvdots(1+(3)/(1))(1+(5)/(4))(1+(7)/(9))...(1+((2n+1))/(n^(2)))=(n+1)^(2)

Prove the following by using the Principle of mathematical induction AA n in N 4^(n) +15n-1 is divisble by 9.

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(2)+(1)/(4)+(1)/(8)+...+(1)/(2^(n))=1-(1)/(2^(n))

Prove the following by the principle of mathematical induction: 2+5+8+11++(3n-1)=(1)/(2)n(3n+1)

CBSE COMPLEMENTARY MATERIAL-PRINCIPAL OF MATHEMATICAL INDUCTION -Short Answer Type Questions
  1. If P(n) is the statement n^2-n+41 is prime. Prove that P(1),\ P(2)a n ...

    Text Solution

    |

  2. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  3. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  4. Prove the following by the principle of mathematical induction: a+(...

    Text Solution

    |

  5. Prove the following by the principle of mathematical induction: 7+7...

    Text Solution

    |

  6. sin x+sin 2x + sin 3x+...+ sin nx =(sin((n+1)/2)xsin(nx)/2)/sin(x/2)

    Text Solution

    |

  7. Using principle of mathematical induction prove that cosalpha\ cos2...

    Text Solution

    |

  8. Prove the following by the principle of mathematical induction: 1^2...

    Text Solution

    |

  9. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  10. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  11. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  12. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  13. 1 1^(n+2)+1 2^(2n+1) is divisible by 133.

    Text Solution

    |

  14. Using the principle of mathematical induction. Prove that (x^(n)-y^(n...

    Text Solution

    |

  15. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  16. 7^(2n) + 2^(3n-3).3^(n-1) is divisible by 25

    Text Solution

    |

  17. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  18. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  19. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  20. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |