Page 34 - Math Grade 11 (Advance)

PROEUS DARA

t~mmrifin.nri~~6i9tsril~:n-1Sl6i (x+ y)" ~
u u u ""
n n ? n - 1 1 ? n - 2 2 ? n - r r l n
( x+y =x+.x y+.x y+ ... +.x y+ ... +y
1
)
2 3 (r+l) ... (n+I)
lxn n(n- 1) n(n-l)(n-2) ... (n-r+ I) ... I
UlHH'tHHlJl 1
I 1 1x2 lx2x3x ... xr
n n n-1 1 n(n-1) n-2 2 n(n-1)(n-2) ... (n-r+ 1) n-r r l n
= 1 X +-X y + 1 2 X y + ... + 1 2 3 X y + ... + y
I x x x x ... xr
t:lmsg
u
n _ I n n n-1 1 n(n-1) n-2 2 n(n-l)(n-2) ... (n-r+ 1) n-r r l n
( X+ y ) - X +-~X y + 1 2 X y + ... + 1 2 3 X y + ... + y
x x x x ... xr
chfitmn.nfruum5 t~tllimtntn52 m~n.n t2t9mctl~22 ttl rut~ot5~& ff1 ttii rut~'e~m
L.:i n ......, 1 () u "" ..
1
n!
I = ._..,- , = C(n, 0) = C(n, n)
n . 0.
n n!
I = (n _ I)! 1! = C(n, 1) = C(n, n- 1)
n(n- I) _ n ! _ . _
. - ( _ ) • - C( n ,2) - C( n, n - 2)
I 2 .. n 2 1 21 .
.
n(n- I )(n- 2) _ n! _ _
l x2x3 - (n-3)!3!- C(n,3)- C(n,n-3)

n(n- I)(n-2) ... (n-r+ 1) _ n! _ C( ) _ C( )
~___,.~,...--~~---'- - - n r - n, n- r
Ix2x3x ... xr (n-r)!r! '
~22tt:H C(n,O), C(n,l), C(n,2), ... , C(n,n)ttnictltru2t'l§~Mt2&9m(x+yt
U I ()

n _ n ~ n-1 1 n(n-1) n-2 2 n(n-l)(n-2) ... (n-r+ 1) n-r r n
( X+ y ) - 1 X +IX y + 1 2 X y + ... + 1 2 3 X y + ... + 1 y
/ x ~ x x x ... xr ~
n ( f ) n-1 1 \( n-2 2 ) n-r r ( ) n
C(n,O)x +C n, 1 x y +C n,2)x y + ... +C(n,r x y + ... +C n,n y)

n
) n - I 1
(
) n
(
) n - 2 2
(
) n
) n - r r
(
n
(
""'
( x + y = L., C n,r x y = C n ,0 x + C n, 1 x y + C n, 2 x y + ... + C n, n y
)
r=O