1 - a
1 - r1 - r

though always less than

1
1 - r

may be brought as near to

1
1 - r

as we please; that is, the series 1 + r + rr + &c. continually approaches to the limit

1 .
1 - r

Thus 1 + ½ + ¼ + ⅛ + &c. where r = ½, continually approaches to

1or 2,
1 - ½

as was shewn in the last article.