E-Storesome important shrtcts...BINOMIAL
hii frnds...
i knw most of u hate binomial theorem chapter...
so here are some pts that will help u....in ur exams...
1) To find the greatest term in the expansion of (1 + x)n
i) calculate .. [ |x| (n+1)] / |x| + 1
if m comes out to be an integer then , Tm & Tm+1 are equal and both are greatest term
if m is nt an integer , then T[m+1] is the greatest term
, where [.] is the greatest integral part
take and example
greatest term in (2 + 3x)9 wen x = 3/2 is....
now just calculate the value
(2 + 3x)9 = 29 [1 + 3x/2]9
as x = 3/2
= [1 + (9/4)]9calculate m now
m = |9/4| (9+1) / [|9/4) + 1]
m = 90/13
wich is nt an integer
so greatest term = Tm+1 = T6+1 = T7....
2) greatest term in the expansion (x + y)n
= ( 1 + (y/x))n
3)If n is even , greatest coeff = nCn/2
if n is odd , greatest coeff are , nC(n-1)/2 & nC(n+1)/2
4)The sum of binomial coeff in the expansion (1 + x)n is 2n
5)The sum of coeff of odd terms in the exp (1 + x)n is = to sum of coeff of even terms and each = to 2n-1
6)the coeff of a1n1, a2n2............amnm in the exp of ( a1 + a2 + .......am)n is
= n! / n1! n2!....nm!
7)If (1 + x)n = Co + C1x + C2x2 + .......... + Cnxn....
u can use integration also here
i) if sum contains Co , C1 ,C2...........Cn are all +ive signs , then integrate b/w limits 0 to 1
ii)If sum contains alternative signs ( + and -) then integrate b/w limits 0 and -1
iii) if sum contains odd coeff Co C2...etc then integrate b/w -1 to +1
iv) if sum contains even coeff C1 C3...then subtracting (ii) frm (i) and then dividing by 2
P.S this method is only applicable wen numericals ccur as denomenator of the binomial coeff...
if u r nt clear...tell me i will show u by an example...
HOPE THIS HELPS.....
ALL THE BEST
CHEERS!!!!!!!!!!!!!!!!
Comments (12)
i lyk ths colour :)
lol.....
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except the text colour isnt that goood..jus kiddin