Page 36 - Math Grade 11 (Advance)

PROEUS DARA
n-1
- ~n (b 11 ) ttltHli!Utl~nrutllti 1 tS~n (an) ti:lru an= a 1 + ~ bk , n:::::2 '1
k = 1
n-1
- fi}n (en) ttldru!Ubfi}nrutllli 2 tsfijn (an) ti:lru an= a1+ ~bk, n:::::2 '1
1 I I k = l

n-1
- ttfirufijn (b") ttldru!Utlfi}nrutllti ts fi}n (an) tel ru bn = b1 + ~ ck
I I
I k = 1
n::::: 2 '1
0 1 0 0 OJ .c::i,J I eJ 0 I e/':J ~ OJ
- 92lfi9StlntrulSI!lttlUJl'iHI:ln5i'Hliln~ an+ 1 ttlH~I!l't!StS~ an tS~n (an) '1
1
0 .o 0 OJ '
- 92ln9Stlntrul29~tl ak+ 1 = pak+q (p, q ton

tltrutlt9ittl ak+ -c = p(ak-c) ti:ln5'i:flS!U~fil~nhflru c = pc+q '1
1
0 ,o 0 Ql • C» eJ
- 92ln9Stlntrul29~tl an+I = an+pn t218dn5hltl~n (b ) ti:lru
11
I
n-l n-1
bn = an+ 1-an = pn 2tJ an= a 1 + ~bk = a 1 + ~pk
k=! k=!
- titmg n::::2 tl!ltnS Sn-Sn-I =an Sti S = a 1
1
0 10 0 OJ ':I OJ t Ql Q I
92ln9Stlntrul2tS~n (an) 9~b an+ +pan+l +qan = 0 'i:flS!U'efillhlffln5
2
1
2
x +px+q = 0 tl:lruyhl a 2tJ 13 tltt1Q)n5~2Cl.Q a+l3 = -p , al3 = q &21&
tl!ltnS an+ -(a+l3)an+ 1 +al3an = 0 ~f!Utltrubttl
2

0 aO 0 cJ1 QJ C»
92ln9Stl9ltl 2 tS81!1ttl~nr:uM'i:flUi '1
I

(i) P(n) tlncrtm& n = 1
0
(ii) 2'i5'i:flrtl P(n) nncrtmg~l!lU n = k wummm P(n+ 1) "" nnmmgUlu
LJ
u
•
lll ....,
n = k+ 1 '1

n
(x + y/ = ~ C(n, r)xn-r /
r=O
(
) n
(
n
) n-r r
) n-1 1
(
= C ( n, 0 x + C n, 1 x y + ... + C n, r x y + ... + C n, n y
)
31