TRACT 9

ALL THEIR TERMS POSITIVE

207

fitter to receive the application of the theorem. Thus tocollect the first 12 terms:

No.

Powers of x.

1

•9 - - - -

2

•81 - - - -

3

•729 - - - -

4

•6561 - - -

5

•59049 - - -

6

•531441 - -

7

•4782969 - -

8

•43046721 - -

9

•387420489

10

•3486784401 -

11

•31381059609 -

12

•282429536481

13

•2541865828329

The first 12 terms, found by dividing x, *3,•9 &c, by the numbers 1, % 3, &c,

•405

•243

•164025

•1 18098

•0885735

•06832812857

•05380840125

•043046721

•03486784401

•02852823601

•02353579471

2*17081162555 the sum of 12 terms.

Then we have to find the sum of the rest of the terms afterthese first 12 , namely of x 11 x ( X V +- r V 1 ’ + -rV r2 + rs - r3 + &<"•)»in which x — - 9, and x is — ‘2541865828329 ; also a = Yj-,b — -jly, c = T V, &c, and the first application of our rule,gives, for the value of + Y 3 V + &c, or s >

(tY)'-—- 005917159763 &c

•012637363—v' 1 x:-Ut)034(J136+ D00279397r+OOU233592i a +&C

the second gives

•00591715976

•012637363

•000340136V

the third sri

•O0U088678 - ** x : -000004086 + -000003060x + &c :

gives

•00591715976

"012637363 —-

•000340136V

•000088678-

•000004087V

the fourth gives

•000001333--V x :'000000089+ &C

•00591715976

"012637363-

•000340136V

•000088678 —

000004087V

• 000001333 -•

•00(,000089V•0000000344’