Where the law of formation of the several terms of

the series is sufficiently evident.

2. It is required to convert

b)-2, into an infinite series.

1

(a + b) 2'

or its equal (a+

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

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

4. It is required to convert 2/9, or its equal (8+1) into an infinite series.

5. It is required to convert 2, or its equal ✔✅(1+1),

into an infinite series.

Ans. 1+

3.5.7

+

-&c.

1 1 3
3.5
+
2 2.4 2.4.6 2.4.6.8 2.4.6.8.10

6. It is required to convert 3/7, or its equal (8—1)3,

into an infinite series.

7. It is required to convert 5/240, or its equal (243-3), into an infinite series.

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

9. It is required to convert (a+b) into an infinite

series.

10. It is required to convert (ab) into an infinite

series.

Ans. a3şı

b 362 3.763

3.7.1164

4a 4.8a2 4.8.12a3 4.8.12.16a4

&c. }

11. It is required to convert (a+x) into an infinite

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

series.

13. It is required to convert.

(a+x) into an infinite series.

5.10.15.20

(a±x)=

Ans.

x 3x2 +.

2a 2.4a2 2.4.6a3 2.4.6.8a4

14. It is required to convert

글 into an infinite series.

Ans. a1+:

2.5x3 2.5.8 4

3a 3.6.a2 可 3.6.9a3 3.6.9.12a4

+

+ &c. }

1

15. It is required to convert

or its equal

(1+x)*

(1+x)

x 6x2 - 6.9x3

5.10 5.10.15 5.10.15.20

16. It is required to convert (a+a),

(a+x) (a2 --- x2)**, into an infinite series.

or its equal

x x2 x3 3x4, 3x5 5.x8 5x7 Ans. + -+ + + +: +. &c. a 2a2 2a3 8a4 8a5 16x6 1647