m-an

CQ=

13 n

2
2 2

22
BQ=

X-X
2n

2a a? 2.403
22

3x3

X 3n

-D,

2.403 a 2.4.605 in- -3n 1-6 3x3

3.5x4 -DQ

Х

Х 4n

8 2.4.625 a2 2.4.6.8a? in - 4n 1 8 3,5x4

2 3.5.7x5
EQ
x

x 5n

10 2.4.6.8a7 a 2.4.6.8.10ao &c.

&c.

&c.
Therefore (a2+)=
x2

3.5x4 3.5.725 at

-&c. 2a 2.4a3 2.4.6a5 2.4.6.8a7 2.4.6.8.1009 Where the law of formation of the several terms of the series is sufficiently evident.

1 2. It is required to convert or its equal (a to

(a + b)2' b)->, into an infinite series.

b
and

2, or m=-2 and n=1; whence

3x3

S

+

+

m

Here e=a, e=

.

the first of these expressions may be exhibited in the more simple form

m(m -- 1) m(m-1) (a+x)m=amtmamis+ am-log3 +

1 2

1.2 (in-2)

am-3x3.

3 min-1) (

m2) [m-(n-1)]a"zmas

1... 3 4 Where the last term is called the general term of the series, bem caus- if 1 2, 3, 4, &c. be substituted successively for n, it will give all the rest.

o

4. It is required to convert V9, or its equal (8+1)*

into an infinite series.

Therefore 9= 1 1

5 2+

3.22 3.6.24 ' 3.6.9.27 3.6.9 12.210

5.8

3.6.20+

5.8.11 + 3.6.9. 12.15.2 13

&e.

5. It is required to convert V/2, or its equal „(1+1), into an infinite series.

1 1 3 3.5 3.5.7 Ans. 1+

&c. 2 2.4'2.4.6 2.4.6.8 2.4.6.8.10

+

+

6. It is required to convert 77, or its equal (8-1)},

into an infinite series.

1

1 Ans. 2

3.22 3.6.24

7. It is required to convert 240, or its equal (243 - 3)}, into an infinite series.

1
4
4.9

4.9.14 Ans. 3

&c. 5.33 5.10.37 5.10.15.311 5.10.15.20.315

8. It is required to convert (a=x)# into an infinite

series.

b 262 3a 3.6a2

+

2.563 3.6.9.a3

2.5.864 3.6.9.1204

9. It is required to convert (a+b)# into an infinite series. Ang. af{1+ }

&c.} 10. It is required to convert (a−b)# into an infinite

Ans. at{1

ał

series.

6 362 40 4.8a?

3.763 4.8,12a3

3.7.1164 4.8.12.1694

-&c.}

11. It is required to convert (a+w)$ into an infinite series. 230 23

4.723 4.7.1035 Ans.a?{1+

ta
-+

-&c.} За 9a2 92 a3 92 12a" 92.12.15a5

4x3

12. It is required to convert (1-2)} into an infinite

series.

Ans. 1.

2.3x2 2.3.8x3 2.3.8.13x4
5.10 5.10.15 5.10.15.20

&c.

5

1 13. It is required to convert

or its equal

(a£x)? (a+x)-7 into an infinite series.

3x2 3.5x 3 3.5.7x4 Ans. {

ti + &c.} 20' 2.402 2.4.6a3' 2.4.6.894

+

十

a

14. It is required to convert

or its equal

(a +2)$ (a+x)into an infinite series. 1

2x3 2.5x3 2.5.8.04 Ans. a}{17+

3a +3.6.az F3.6.9937 3.6.9.12a4

F &c.}

1 15. It is required to convert

or its equal

(1+x)} (1+x)} into an infinite series.

6x? 6.9x3 6.9.14x4
Ans. 1.
+
:t

.&c. 5 5.10 5.10.15 5.10.15.20

ata)', or its equat

16. It is required to convert ( (a +x) (a2--2a), into an infinite series.

X2 23

3x4, 3x5
Ans. -+
+

十三 te
2a3894
2a2

.&c. 805' 16x6. 1697

5х в

5х7

+

it