E-StoreBINOMIAL THEOREM{1}
31 May 2007 22:28:21 IST
BINOMIAL THEOREM{1}
1.Coefficient of xm in the expansion of {axp + b/xq}n is the coefficient of Tr+1 where r=np-m/p+q
to get the independent term of the above expansion put m=0
2.The coefficient of xn-1 in the expansion of (x-1)(x-2)(x-3).....(x-n) is -n(n+1)/2.
3.The coefficient of xn-1 in the expansion of (x+1)(x+2)....(x+n) is n(n+1)/2.
4.If the coefficients of rth,(r+1)th,(r+2)th terms of (1+x)n are in A.P. then
(n-2r)2=n+2
5.The rth term from the end of (1+x)n is the (n-r+2)th term from the beginning
6.Sum of the coefficients of (ax+by)n is (a+b)n.
7. The no.of rational terms in the expansion of ([p ]
a+[q ]b)n is
a+[q ]b)n is [ n/L.C.M of p&q] +1 where[.] =step function.
8.The no.of non-zero terms in the expansionj of
i} (x+a)n + (x-a)n is 1) n+1/2 if n is odd
2)n/2+1 if n is even
ii}(x+a)n - (x-a)n is 1)n+1/2 if n is odd
2)n/2 if n is even
9.Coefficient of xp.yq.zr.ts in the expansion of (ax+by+cz+dt)n (where p+q+r+s=n) is n!/p!q!r!s! . ap.bq.cr.ds.
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THANKS IN ADVANCE.....
Comments (18)
Himanshu
Forum Expert
Joined: 19 Feb 2007 19:24:42 IST
Posts: 3834
31 May 2007 22:44:43 IST
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coooooooooooooooooooooooollllllllllllllllllllllllllllllllllllll
8 Mar 2009 11:48:55 IST
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More!!!!!!!!!!!!!WIll GIVE YOU A THOUSAND RATES ANY DAY!!!!!!!!!!!
11 Mar 2009 16:02:21 IST
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its really awesome nd helpful ... such articles shudn't be lost in d shelf !!!
16 Feb 2010 23:24:27 IST
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its gr8 .....can u also write an article on summation of series in bt?
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