some important pts. while u r doing binomial theorem.............

 

1) ⁿc_r is maximum for a given value of n  r

a) wen n is even ............r = n/2

b)wen n is odd ..............r = n+1/2 or n-1/2

 

2)co-eff. of terms equidistant frm the beginning and end in the expansion of (x + a)ⁿ are equal

 

3)(1+x)^-k  = ^{k + r - 1}c_r . x^r

 

4)no. of dissimilar terms in the expansion of (x + y + z)ⁿ is ( n + 1 )( n + 2 ) / 2

 

5)In the expansion of (x + a)ⁿ (x , a >0 ) the greatest term is T_m+1 where m is the largest +ive integer 'r' satisfying [n-r+1.a] / rx >= 1

 

6)if x > 0 ,  then the greatest co-eff. in the expansion of (1+x)ⁿ is

a)ⁿc_n/2 if n is even

b)ⁿc_(n-1)/2 or ⁿc_(n+1)/2 if n is odd

 

7 ) If the index 'n' is even then there is only 1 middle term in the expansion of (x+a)ⁿ i.e = (n+2)/2 th term

 

8)If the index 'n' is odd, then there are 2  middle terms in the expansion of (x+a)ⁿ i.e = (n+1)/2th and (n+3)/2th terms

 

9)sum of co-eff. in the expansion of (x+a)ⁿ is 2ⁿ

 

10)sum of co-eff. of odd terms = sum of coeff of even terms i.e 2^n-1

 

original

no copy paste

wrote myself

hope these helps......................