Home
Class 11
MATHS
Using binomial theorem, prove that (101)...

Using binomial theorem, prove that `(101)^(50)> 100^(50)+99^(50)dot`

Text Solution

Verified by Experts

The correct Answer is:
N/a
`(105)^(50)-(100^(50)+90^(50))`
`=101^(50)-100^(50)-99^(50)`
`=(100+1)^(50)-(100-1)^(50)-100^(50)`
`=[100^(50+50)C_(1).100^(49)+^(50)C_(2).100^(40)`
`.......+^(50)C_(49).100+1]-[100^(50)`
`-^(50)C_(1).100^(49)+^(50)C_(2).100^(48)`
`+....-^(50)C_(49).100+1]-100^(50)`
`=2xx^(50)C_(1)xx100^(49)+2xx^(50)C_(3)xx100^(47)`
`+......+2xx^(50)C_(49)xx100-100^(50)`
`=2xx^(50)C_(3)xx100^(47)+....+2xx^(50)C_(49)xx100gt0`
`:.101^(50)-(100^(50)+99^(50)) gt 0`
`rArr " "101^(50)gt 100^(50)+99^(50)`
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 8A|22 Videos

  • BINOMIAL THEOREM

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 8B|38 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|20 Videos

Similar Questions

Explore conceptually related problems

Using binomial theorem, evaluate : (101)^4

Using binomial theorem, evaluate : (102)^5

Using binomial theorem compute : (10. 1)^5

Using binomial theorem compute : (102)^6

Using the binomial theorem, evaluate (102)^5 .

Use binomial theorem to evaluate (10.1)^(5) .

Using binomial theorem, evaluate : (99)^5

Using binomial theorem, evaluate : (96)^3

Using binomial theorem compute : (99)^5

Using binomial theorem find (i) (101)^(5) (ii) 51^(6)

NAGEEN PRAKASHAN ENGLISH-BINOMIAL THEOREM-Miscellaneous Exericse
  1. Using binomial theorem, prove that (101)^(50)> 100^(50)+99^(50)dot

    Text Solution

    |

  2. Find a, b and n in the expansion of (a+b)^nif the first three terms ...

    Text Solution

    |

  3. If the coefficients of x^2a n d\ x^3 in the expansion o (3+a x)^9 are ...

    Text Solution

    |

  4. Find the coefficient of a^4 in the product (1+a)^4(2-a)^5 using binomi...

    Text Solution

    |

  5. If a and b are distinct integers, prove that a - b is a factor of a^n-...

    Text Solution

    |

  6. Evaluate (sqrt(3)+sqrt(2))^6-(sqrt(3)-sqrt(2))^6dot

    Text Solution

    |

  7. Find the value of (a^2+sqrt(a^2-1))^4+(a^2-sqrt(a^2-1))^4.

    Text Solution

    |

  8. Find an approximation of (0. 99)^5 using the first three terms of its ...

    Text Solution

    |

  9. Find n, if the ratio of the fifth term from the beginning to the fi...

    Text Solution

    |

  10. Using binomial theorem expand (1+x/2-2/x)^4,\ x!=0.

    Text Solution

    |

  11. Find the expansion of (3x^2-2a x+3a^2)^3 using binomial theorem.

    Text Solution

    |

  12. Find a, b and n in the expansion of (a+b)^nif the first three terms ...

    Text Solution

    |

  13. If the coefficients of x^2a n d\ x^3 in the expansion o (3+a x)^9 are ...

    Text Solution

    |

  14. Find the coefficient of x^5 in the expansion of (1 + 2x)^6 (1-x)^7.

    Text Solution

    |

  15. If a and b are distinct integers, prove that a - b is a factor of a^n-...

    Text Solution

    |

  16. Evaluate (sqrt(3)+sqrt(2))^6-(sqrt(3)-sqrt(2))^6dot

    Text Solution

    |

  17. Find the value of (a^2+sqrt(a^2-1))^4+(a^2-sqrt(a^2-1))^4.

    Text Solution

    |

  18. Find an approximation of (0. 99)^5using the first three terms of its ...

    Text Solution

    |

  19. Find n, if the ratio of the fifth term from the beginning to the fi...

    Text Solution

    |

  20. Expand using Binomial Theorem (1+x/2-2/x)^4,x!=0.

    Text Solution

    |

  21. Find the expansion of (3x^2-2a x+3a^2)^3 using binomial theorem.

    Text Solution

    |