4.2 Sum and Sigma notation
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calc 1 notes and exercises, Exercises of Calculus
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4.2 Sum and Sigma notation
^
Sigma notation :
20 end [ 2
formula
12+22+
... -
index I =L of summation a) ' ° start i.
Ti
, b) 3 ? A) 3 -15+7+9+
Theorem 2.1 :
b) SinC4lt ) + Sin ( 61T
-1 sin @ it ) + Sincloit ) + sin U2ñ)=
If
" n " is any Positive
integer
and " C " is
any constant
, then , C)
n C= Cn ( Sum of constant )
Li )
e- I 5
ii ) "
i=nCn -11) (
sum of the first " n "
integers )
c. 0=511-- -1= 2 3 j2= (3) (4) (7) = 14
Cii
)
I.
it _-
ncn
)
(
2n -11 ) (
sum of the squares of the first " n "
Positive integers]
± ,
8 A) 2 e.
it
7=11-- (8%9)+(1×8)= final answer b) ' 2%
Theorem 2.2 i
g. i
"° c. I = 2180071801 )
- ( 800 )( 1) = 641, final answer 2 n n
for
any constant
" C " & d , g. ( Ca :
dbi
)=C
c. ai + d ?=±bi . a) 20121
413= > final answer 6 10 10 10 10 c- z= ) " FCO. Ii ) = g. ( 0.1 +3=0. g.
it
3=(0.01310111×21)
(b) = 33.8s b) " 18--4%(20%417)=7. > final answer j= i= 6 final answer Ex : - what if
i -1-
?
~ 5
= j = , , > c-
2--0.95-10 - Ii , for c- = 1, ,
...
> 20 . 20 g. f- ( 0.95+0.
= ÷, [ 310.95+0.1 i } -410.95-10 - Ii} -12] = 110.030+0.17-[1-0.9075]=0. " c- 2+0. ?° i -1%10.
I = s
i.
=3 c.
( I -12 ) =
I
¥ 12
15+10--25 = 0- (201211147-3)+0.17 (2%213)+0.
= 139.95 > final answer 6
5 i = g.
i - ] = & i2_4i
= ¥%i2+& 4i