11X1 T14 06 sum of a geometric series (2010)
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Transcript of 11X1 T14 06 sum of a geometric series (2010)
![Page 1: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/1.jpg)
Sum Of A Geometric
Series
![Page 2: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/2.jpg)
Sum Of A Geometric
Series 12 n
n arararaS
![Page 3: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/3.jpg)
Sum Of A Geometric
Series 12 n
n arararaS nn
n arararararrS 132
![Page 4: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/4.jpg)
Sum Of A Geometric
Series 12 n
n arararaS nn
n arararararrS 132
aarSr n
n 1
![Page 5: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/5.jpg)
Sum Of A Geometric
Series 12 n
n arararaS nn
n arararararrS 132
aarSr n
n 1
1
1
r
raS
n
n
![Page 6: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/6.jpg)
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
![Page 7: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/7.jpg)
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
![Page 8: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/8.jpg)
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
![Page 9: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/9.jpg)
Sum To Infinity (Limiting Sum)
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Sum To Infinity (Limiting Sum) 1: rNOTE
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Sum To Infinity (Limiting Sum) 1: rNOTE
0lim ,1 If
n
nrr
![Page 12: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/12.jpg)
Sum To Infinity (Limiting Sum) 1: rNOTE
0lim ,1 If
n
nrr
r
raS
n
nn
n
1
1limlim
![Page 13: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/13.jpg)
Sum To Infinity (Limiting Sum) 1: rNOTE
0lim ,1 If
n
nrr
r
raS
n
nn
n
1
1limlim
r
a
1
![Page 14: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/14.jpg)
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
![Page 15: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/15.jpg)
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
![Page 16: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/16.jpg)
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
![Page 17: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/17.jpg)
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
![Page 18: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/18.jpg)
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
![Page 19: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/19.jpg)
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
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8
3
1
2
16
n
n
ii
![Page 21: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/21.jpg)
8
3
1
2
16
n
n
ii2
2
16
a
![Page 22: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/22.jpg)
8
3
1
2
16
n
n
ii2
2
16
a
2
3
![Page 23: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/23.jpg)
8
3
1
2
16
n
n
ii2
2
16
a
2
3
6 ,2
1 nr
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8
3
1
2
16
n
n
ii2
2
16
a
r
raS
n
n
1
12
3
6 ,2
1 nr
![Page 25: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/25.jpg)
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
![Page 26: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/26.jpg)
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
![Page 27: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/27.jpg)
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
![Page 28: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/28.jpg)
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
![Page 29: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/29.jpg)
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
![Page 30: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/30.jpg)
8
1
4
1
2
1 iv
![Page 31: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/31.jpg)
8
1
4
1
2
1 iv
2
1,
2
1 ra
![Page 32: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/32.jpg)
8
1
4
1
2
1 iv
2
1,
2
1 ra
r
aS
1
![Page 33: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/33.jpg)
8
1
4
1
2
1 iv
2
1,
2
1 ra
r
aS
1
1
2
11
2
1
![Page 34: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/34.jpg)
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
![Page 35: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/35.jpg)
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
![Page 36: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/36.jpg)
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
![Page 37: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/37.jpg)
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
![Page 38: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/38.jpg)
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
![Page 39: 11X1 T14 06 sum of a geometric series (2010)](https://reader033.fdocuments.net/reader033/viewer/2022060202/559d08751a28abed478b45e6/html5/thumbnails/39.jpg)
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