Home
Class 11
MATHS
By the Principal of mathematical inducti...

By the Principal of mathematical induction, prove that `1+5+5^2+…..+5^(n-1)=(5^n-1)/4`

Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATIONS

    MAXIMUM PUBLICATION|Exercise EXAMPLE|171 Videos

  • PROBABILITY

    MAXIMUM PUBLICATION|Exercise EXAMPLE|98 Videos

Similar Questions

Explore conceptually related problems

Using the principal of Mathematical induction, prove that 1/2+1/4+1/8+…….+1/2^n=1-1/2^n

(b)Prove by the principle of mathematical induction that 3^n>2^n.

By using mathematical induction prove that 1+4+7+...+(3n-2)=(n(3n-1))/2

Prove by using the principal of Mathematical Induction P(n)=1+3+3^2+…..+3^(n-1)=(3^n-1)/2 is true for all n in N

(b)Prove by principle of mathematical induction that 2+2^3+2^4+……..+2^n=2(2^n-1)

(a)Prove the following by using the principle of mathematical induction for all n in N:2^1+2^2+……..+2^n=2^(n+1)-2 .

Using the principle of Mathematical induction,prove that 10^(2n-1)+1 is divisible by 11.

Using mathematical induction prove that 1^3+2^3+3^3+.....+n^3=[(n(n+1))/2]^2

Prove that by 1.2+2.3+3.4+…..+n(n+1)=(n(n+1)(n+2))/3 by using the principle of mathematical induction for all n in N .

Prove 1.2+2.2^2+3.2^3+………+n.2^n=(n-1)2^(n+1)+2 by using the principle of mathematical induction for all n in N .

MAXIMUM PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-EXAMPLE
  1. Given P(n):3^(2n) 1 is divisible by 8. Is the statement P(n) true f...

    Text Solution

    |

  2. Prove that by 1.2+2.3+3.4+…..+n(n+1)=(n(n+1)(n+2))/3 by using the prin...

    Text Solution

    |

  3. By the Principal of mathematical induction, prove that 1+5+5^2+…..+5^(...

    Text Solution

    |

  4. Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. Verify t...

    Text Solution

    |

  5. Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. By assum...

    Text Solution

    |

  6. Consider the statement P(n):1^2+2^2+3^2+…….+n^2=(n(n+1)(2n+1))/6 C...

    Text Solution

    |

  7. Consider the statement P(n):1^2+2^2+3^2+…….+n^2-(n(n+1)(2n+1))/6 B...

    Text Solution

    |

  8. Consider the statement P(n):1^2+2^2+3^2+…….+n^2=(n(n+1)(2n+1))/6 I...

    Text Solution

    |

  9. Consider the statement P(n)=1+3+3^2+…….+3^(n-1)=frac(3^(n-1))(2) C...

    Text Solution

    |

  10. Consider the statement P(n)=1+3+3^2+…….+3^(n-1)=frac(3^(n)-1)(2) I...

    Text Solution

    |

  11. Consider the statement p(n):1^3+2^3+3^3+………..+n^3=[(n(n+1))/2]^2 V...

    Text Solution

    |

  12. Consider the statement p(n):1^3+2^3+3^3+………..+n^3=[(n(n+1))/2]^-2 ...

    Text Solution

    |

  13. Consider the statement P(n):1.2+2.3+3.4+…….+n(n+1)=(n(n+1)(n+2))/3 ...

    Text Solution

    |

  14. Consider the statement P(n):1.2+2.3+3.4+…….+n(n+1)=(n(n+1)(n+2))/3 ...

    Text Solution

    |

  15. Consider the statement P(n)=3^(2n+2)-8n-9 is divisible by 8 Verify...

    Text Solution

    |

  16. Consider the statement P(n)=3^(2n+2)-8n-9 is divisible by 8 Prove ...

    Text Solution

    |

  17. Consider the statement: P(n)=1^3+2^3+3^3+……..+n^3=[(n(n+1))/2]^2 P...

    Text Solution

    |

  18. Consider the statement: P(n)=1^3+2^3+3^3+……..+n^3=[(n(n+1))/2]^2 I...

    Text Solution

    |

  19. Consider the statement: P(n)=1^3+2^3+3^3+……..+n^3=[(n(n+1))/2]^2 I...

    Text Solution

    |

  20. Using the principal of Mathematical induction, prove that 1/2+1/4+1/...

    Text Solution

    |