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Tuesday, December 9, 2014

BINOMIAL THEOREM FOR POSITIVE INTEGRAL INDEX

If x and a are real , then

i.e

  • General term for is

  • In the binomial expansion of , term from end is term from beginning .
  • If n is odd then no .of terms in . Have equal no. of terms =
  • If n is odd then has terms has terms
  • Middle term in a binomial expansion
    If n is even
    Then middle term of is term
  • If n is odd then Middle terms are and terms
  • STANDARD NOTATIONS
  • Examples based on Integer part and fraction part

  • where

    I ,n Then (I+f) ( I –f) = 1

    Steps to solve these type problems:

    1) write the given expression =I +F

    Where I is Integer ,F is fractional part

    2) Define G by replacing ‘+’ sign by ‘-‘.Note G always lies between 0 and 1

    3) Either add or subtract G from expression in Step -I so that R.H.S is an integer.

    4) G+F = 1 i.e. if G is added G = 1-F

    i.e if G is subtracted then G-F = 0 = G =F

    5) Obtain the value of desired expression given.

Greatest term

Let and and is integral part then

1. If is not a integer , Then is numerically greatest term in the binomial expansion of

2. If is an integer then and are numerically greatest terms in expansion

Largest binomial coefficient :

The largest among is (are ) :

1. If n is event integer then is largest.



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