11 x1 t14 06 sum of a geometric series (2012)
TRANSCRIPT
Sum Of A Geometric
Series
Sum Of A Geometric
Series 12 n
n arararaS
Sum Of A Geometric
Series 12 n
n arararaS nn
n arararararrS 132
Sum Of A Geometric
Series 12 n
n arararaS nn
n arararararrS 132
aarSr n
n 1
Sum Of A Geometric
Series 12 n
n arararaS nn
n arararararrS 132
aarSr n
n 1
1
1
r
raS
n
n
Sum Of A Geometric
Series 12 n
n arararaS nn
n arararararrS 132
aarSr n
n 1
1
1
r
raS
n
n 1 if , r
Sum Of A Geometric
Series 12 n
n arararaS nn
n arararararrS 132
aarSr n
n 1
1
1
r
raS
n
n
OR
1 if , r
r
raS
n
n
1
1
Sum Of A Geometric
Series 12 n
n arararaS nn
n arararararrS 132
aarSr n
n 1
1
1
r
raS
n
n
OR
1 if , r
r
raS
n
n
1
1 1 if, r
Sum To Infinity (Limiting Sum)
Sum To Infinity (Limiting Sum) 1: rNOTE
Sum To Infinity (Limiting Sum) 1: rNOTE
0lim ,1 If
n
nrr
Sum To Infinity (Limiting Sum) 1: rNOTE
0lim ,1 If
n
nrr
r
raS
n
nn
n
1
1limlim
Sum To Infinity (Limiting Sum) 1: rNOTE
0lim ,1 If
n
nrr
r
raS
n
nn
n
1
1limlim
r
a
1
Sum To Infinity (Limiting Sum) 1: rNOTE
0lim ,1 If
n
nrr
r
raS
n
nn
n
1
1limlim
r
a
1
1 if ,1
rr
aS
Sum To Infinity (Limiting Sum) 1: rNOTE
0lim ,1 If
n
nrr
r
raS
n
nn
n
1
1limlim
r
a
1
1 if ,1
rr
aS
1862 of terms10first theof sum theFind .. ige
Sum To Infinity (Limiting Sum) 1: rNOTE
0lim ,1 If
n
nrr
r
raS
n
nn
n
1
1limlim
r
a
1
1 if ,1
rr
aS
1862 of terms10first theof sum theFind .. ige
10 and 3,2 nra
Sum To Infinity (Limiting Sum) 1: rNOTE
0lim ,1 If
n
nrr
r
raS
n
nn
n
1
1limlim
r
a
1
1 if ,1
rr
aS
1862 of terms10first theof sum theFind .. ige
10 and 3,2 nra 1
1
r
raS
n
n
Sum To Infinity (Limiting Sum) 1: rNOTE
0lim ,1 If
n
nrr
r
raS
n
nn
n
1
1limlim
r
a
1
1 if ,1
rr
aS
1862 of terms10first theof sum theFind .. ige
10 and 3,2 nra 1
1
r
raS
n
n
13
132 10
10
S
Sum To Infinity (Limiting Sum) 1: rNOTE
0lim ,1 If
n
nrr
r
raS
n
nn
n
1
1limlim
r
a
1
1 if ,1
rr
aS
1862 of terms10first theof sum theFind .. ige
10 and 3,2 nra 1
1
r
raS
n
n
13
132 10
10
S
59048
8
3
1
2
16
n
n
ii
8
3
1
2
16
n
n
ii2
2
16
a
8
3
1
2
16
n
n
ii2
2
16
a
2
3
8
3
1
2
16
n
n
ii2
2
16
a
2
3
6 ,2
1 nr
8
3
1
2
16
n
n
ii2
2
16
a
r
raS
n
n
1
12
3
6 ,2
1 nr
8
3
1
2
16
n
n
ii2
2
16
a
r
raS
n
n
1
12
3
6 ,2
1 nr
2
11
2
11
2
36
6
S
8
3
1
2
16
n
n
ii2
2
16
a
r
raS
n
n
1
12
3
6 ,2
1 nr
2
11
2
11
2
36
6
S
64
189
1
2
64
63
2
3
8
3
1
2
16
n
n
ii2
2
16
a
r
raS
n
n
1
1
sum? limiting a have 7
2456 Does iii
2
3
6 ,2
1 nr
2
11
2
11
2
36
6
S
64
189
1
2
64
63
2
3
8
3
1
2
16
n
n
ii2
2
16
a
r
raS
n
n
1
1
sum? limiting a have 7
2456 Does iii
156
4r
2
3
6 ,2
1 nr
2
11
2
11
2
36
6
S
64
189
1
2
64
63
2
3
8
3
1
2
16
n
n
ii2
2
16
a
r
raS
n
n
1
1
sum? limiting a have 7
2456 Does iii
156
4r
sum limiting a hasit ,1 as r
2
3
6 ,2
1 nr
2
11
2
11
2
36
6
S
64
189
1
2
64
63
2
3
8
1
4
1
2
1 iv
8
1
4
1
2
1 iv
2
1,
2
1 ra
8
1
4
1
2
1 iv
2
1,
2
1 ra
r
aS
1
8
1
4
1
2
1 iv
2
1,
2
1 ra
r
aS
1
1
2
11
2
1
8
1
4
1
2
1 iv
2
1,
2
1 ra
fraction a as 630. Write v
r
aS
1
1
2
11
2
1
8
1
4
1
2
1 iv
2
1,
2
1 ra
fraction a as 630. Write v
000036.00036.036.063.0
r
aS
1
1
2
11
2
1
8
1
4
1
2
1 iv
2
1,
2
1 ra
fraction a as 630. Write v
000036.00036.036.063.0
01.0 ,36.0 ra
r
aS
1
1
2
11
2
1
8
1
4
1
2
1 iv
2
1,
2
1 ra
fraction a as 630. Write v
000036.00036.036.063.0
01.0 ,36.0 ra
r
aS
1
r
aS
1
1
2
11
2
1
8
1
4
1
2
1 iv
2
1,
2
1 ra
fraction a as 630. Write v
000036.00036.036.063.0
01.0 ,36.0 ra
r
aS
1
r
aS
1
1
2
11
2
1
11
4
99
36
01.01
36.0
8
1
4
1
2
1 iv
2
1,
2
1 ra
fraction a as 630. Write v
000036.00036.036.063.0
01.0 ,36.0 ra
r
aS
1
r
aS
1
1
2
11
2
1
11
4
99
36
01.01
36.0
Exercise 6J; 3cf, 5, 7b
8a(i), 9, 12, 14, 17b
Exercise 6K; 2adgj, 3b,
4a, 6bf, 8, 11a, 17ace, 19*
Exercise 6L, 1dg, 2d, 4a