Sum Of A Geometric Series

Sum Of A Geometric Series

12 nn arararaS

Sum Of A Geometric Series

12 nn arararaS

nnn arararararrS 132

Sum Of A Geometric Series

12 nn arararaS

nnn arararararrS 132

aarSr nn 1

Sum Of A Geometric Series

12 nn arararaS

nnn arararararrS 132

aarSr nn 1

1

1

rraS

n

n

Sum Of A Geometric Series

12 nn arararaS

nnn arararararrS 132

aarSr nn 1

1

1

rraS

n

n 1 if , r

Sum Of A Geometric Series

12 nn arararaS

nnn arararararrS 132

aarSr nn 1

1

1

rraS

n

n

OR

1 if , r

rraS

n

n

11

Sum Of A Geometric Series

12 nn arararaS

nnn arararararrS 132

aarSr nn 1

1

1

rraS

n

n

OR

1 if , r

rraS

n

n

11 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

rraS

n

nnn

1

1limlim

Sum To Infinity (Limiting Sum)1: rNOTE

0lim ,1 If

n

nrr

rraS

n

nnn

1

1limlim

ra

1

Sum To Infinity (Limiting Sum)1: rNOTE

0lim ,1 If

n

nrr

rraS

n

nnn

1

1limlim

ra

1

1 if ,1

rr

aS

Sum To Infinity (Limiting Sum)1: rNOTE

0lim ,1 If

n

nrr

rraS

n

nnn

1

1limlim

ra

1

1 if ,1

rr

aS

1862 ofterms10first theofsum theFind .. ige

Sum To Infinity (Limiting Sum)1: rNOTE

0lim ,1 If

n

nrr

rraS

n

nnn

1

1limlim

ra

1

1 if ,1

rr

aS

1862 ofterms10first theofsum theFind .. ige10and 3,2 nra

Sum To Infinity (Limiting Sum)1: rNOTE

0lim ,1 If

n

nrr

rraS

n

nnn

1

1limlim

ra

1

1 if ,1

rr

aS

1862 ofterms10first theofsum theFind .. ige10and 3,2 nra

11

rraS

n

n

Sum To Infinity (Limiting Sum)1: rNOTE

0lim ,1 If

n

nrr

rraS

n

nnn

1

1limlim

ra

1

1 if ,1

rr

aS

1862 ofterms10first theofsum theFind .. ige10and 3,2 nra

11

rraS

n

n

13

132 10

10

S

Sum To Infinity (Limiting Sum)1: rNOTE

0lim ,1 If

n

nrr

rraS

n

nnn

1

1limlim

ra

1

1 if ,1

rr

aS

1862 ofterms10first theofsum theFind .. ige10and 3,2 nra

11

rraS

n

n

13

132 10

10

S

59048

8

3

1

216

n

n

ii

8

3

1

216

n

n

ii2

216

a

8

3

1

216

n

n

ii2

216

a

23

8

3

1

216

n

n

ii2

216

a

23

6 ,21

nr

8

3

1

216

n

n

ii2

216

a

rraS

n

n

11

23

6 ,21

nr

8

3

1

216

n

n

ii2

216

a

rraS

n

n

11

23

6 ,21

nr

211

211

23 6

6

S

8

3

1

216

n

n

ii2

216

a

rraS

n

n

11

23

6 ,21

nr

211

211

23 6

6

S

64189

12

6463

23

8

3

1

216

n

n

ii2

216

a

rraS

n

n

11

sum? limiting a have 72456 Does iii

23

6 ,21

nr

211

211

23 6

6

S

64189

12

6463

23

8

3

1

216

n

n

ii2

216

a

rraS

n

n

11

sum? limiting a have 72456 Does iii

1564r

23

6 ,21

nr

211

211

23 6

6

S

64189

12

6463

23

8

3

1

216

n

n

ii2

216

a

rraS

n

n

11

sum? limiting a have 72456 Does iii

1564r

sum limiting a hasit ,1 as r

23

6 ,21

nr

211

211

23 6

6

S

64189

12

6463

23

81

41

21 iv

81

41

21 iv

21,

21

ra

81

41

21 iv

21,

21

ra

raS

1

81

41

21 iv

21,

21

ra

raS

1

1211

21

81

41

21 iv

21,

21

ra

fraction a as 630. Write v

raS

1

1211

21

81

41

21 iv

21,

21

ra

fraction a as 630. Write v 000036.00036.036.063.0

raS

1

1211

21

81

41

21 iv

21,

21

ra

fraction a as 630. Write v 000036.00036.036.063.0

01.0 ,36.0 ra

raS

1

1211

21

81

41

21 iv

21,

21

ra

fraction a as 630. Write v 000036.00036.036.063.0

01.0 ,36.0 ra

raS

1

raS

1

1211

21

81

41

21 iv

21,

21

ra

fraction a as 630. Write v 000036.00036.036.063.0

01.0 ,36.0 ra

raS

1

raS

1

1211

21

1149936

01.0136.0

81

41

21 iv

21,

21

ra

fraction a as 630. Write v 000036.00036.036.063.0

01.0 ,36.0 ra

raS

1

raS

1

1211

21

1149936

01.0136.0

Exercise 6J; 3cf, 5, 7b8a(i), 9, 12, 14, 17b

Exercise 6K; 2adgj, 3b,4a, 6bf, 8, 11a, 17ace, 19*

Exercise 6L, 1dg, 2d, 4a