Home
Class 11
MATHS
Using the principle of mathematical indu...

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

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

Similar Questions

Explore conceptually related problems

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

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

By the principle of mathematical induction prove that 3^(2^(n))-1, is divisible by 2^(n+2)

Using principle of mathematical induction , prove that , (x^(2n)-y^(2n)) is divisible by (x+y) fpr all n in N .

Using principle of mathematical induction , prove that n^(3) - 7n +3 is divisible by 3 , for all n belongs to N .

Using principle of mathematical induction prove that x^(2n)-y^(2n) is divisible by x+y for all n belongs to Ndot

Using the principle of mathematical induction, prove that n<2^n for all n in N

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

Prove by the principle of mathematical induction that: n(n+1)(2n+1) is divisible by 6 for all n in Ndot

Prove the following by the principle of mathematical induction: \ 5^(2n)-1 is divisible by 24 for all n in Ndot

CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Find (i) the last digit, (ii) the last two digits, and (iii) the last ...

    Text Solution

    |

  2. If 10^m divides the number 101^(100)-1 then, find the greatest value o...

    Text Solution

    |

  3. Using the principle of mathematical induction, prove that (2^(3n)-1) i...

    Text Solution

    |

  4. If x is very large as compare to y , then prove that sqrt(x/(x+y))dot...

    Text Solution

    |

  5. Find the coefficient of x^n in the expansion of (1-9x+20 x^2)^(-1)dot

    Text Solution

    |

  6. Prove that the coefficient of x^r in the expansion of (1-2x)^(-1/2) is...

    Text Solution

    |

  7. Find the sum: 1-1/8+1/8xx3/(16)-(1xx3xx5)/(8xx16xx24)+...

    Text Solution

    |

  8. Show that sqrt3 =1+1/3+(1/3).(3/6)+(1/3)*((3/6)*(5/9)*(7/12)+.......

    Text Solution

    |

  9. Assuming x to be so small that x^2 and higher power of x can be neg...

    Text Solution

    |

  10. Find the sum sumsum(0lt=i < jlt=n-1)j^n Cidot

    Text Solution

    |

  11. Find the condition for which the formula (a+b)^m = a^m+m a^(m-1)b+(m(...

    Text Solution

    |

  12. Find the value of x , for which 1/(sqrt(5+4x)) can be expanded as infi...

    Text Solution

    |

  13. Find the fourth term in the expansion of (1-2x)^(3//2)""dot

    Text Solution

    |

  14. Prove that .^n C0 . ^(2n) Cn- ^n C1 . ^(2n-2)Cn+^n C2 . ^(2n-4)Cn-=2...

    Text Solution

    |

  15. Prove that ^n C0 .^n C0-^(n+1)C1 . ^n C1+^(n+2)C2 . ^n C2-=(-1)^ndot

    Text Solution

    |

  16. Find the sum of the coefficients of all the integral powers of x in th...

    Text Solution

    |

  17. If the sum of the coefficient in the expansion of (alpha^2x^2-2alphax+...

    Text Solution

    |

  18. Prove that sum(alpha+beta+gamma = 10) (10 !)/(alpha!beta!gamma!)=3^(10...

    Text Solution

    |

  19. If (1+x-2x^2)^(20)=a0+a1x+a2x^2+a3x^3+...+a(40)x^(40), then find the v...

    Text Solution

    |

  20. Find the sum of the series .^15 C0+^(15)C1+^(15)C2+...............+^(1...

    Text Solution

    |