Page 12 - Math Grade 11 (Advance)

PROEUS DARA

n
n. ~ = nc
c
k =I
n n n n n n
~. ~ (ak + bk) = 2: ak + 2: bk '1.15. 2: (ak- bk) = 2: ak- 2: bk
k=l k=l k=l k=! k=l k=l
n n n n
b. ,L (ak + bk) = 2: a~+ 2 2: akbk + 2: b~
2
k=l k=l k=l k=l

n
n. 2: c = c + c + c + ... + c = nc
k =I

n n
2. ,L cak = ca + ca 2 + ca + ... +can = c(a + a + a + ... +an) = c 2: ak
1
1
3
2
3
k = 1 k =I
n
~. 2(ak+bk) = (a 1 +b )+(a 2 +b )+ ... +(an+bn)
1
2
k = 1
n n
= (a 1 + a 2 + ... +an)+ (b 1 + b 2 + ... + bn) = 2: ak + 2: bk
k =I k =I
n
'1.15. 2(ak-bk) = (a -b )+(a -b )+(a -b )+ ... +(an-bn)
3
3
2
1
1
2
k= 1

n n n n n
b. 2 (ak + bk) = 2: (a~+ 2akbk + b~) = 2: a~+ 2: 2akbk + 2 b~
2
k=l k=l k=l k=I k=I

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