11x1 t14 06 sum of a geometric series (2011)

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Sum Of A Geometric Series

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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