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CHAPTER III--PRACTIONS
66
three, the first and the last donowinators we obtained Wing (however multipliert (again, by 2 and respectively.
Examples in illustration thereof. 76. The sum of five or six or seven (ilifferent fractioual) quantities, having l fot (ouch of) their umemtors, is 1 (in each case).. () you, who know arithmetic, say what the required) donominators are.
The rule for finding out the denominators in the case of an mnoven number of fractione) :
77. When the sum of the different fruitional, quantities, having one for oach of their nuncrators, is one, the required) denominatong are such as, beginning with two, go on a successively rising in value by one, each (such denominator) being further) multipliol by that
AK!
From thin it is clear that, wlun the firme fraction ou
the last fraction
are added to this lust rosult, the um boumon 1.
In this connection it may be noted that, in a series in geometrical progression consisting of n terms, having us the first toru and the common ratlo, the
vum in, for all positive integral values of a, loan thun
(n + 1)th term in the series.
Therefore, if we udel to the sum of the series in
geometrical progressivu
, x the (+ 11th torm, which in the lunt fraction
necording to tbe rule stated in this stanza, weet,
have to adi -
in order to get I am tlir om. Things
in oneineet in this
rulo as the first fraction, and wo 3 in the valne chun for a, nince the numerator of all the fractions has to be l.
17. Bere noteszi mitrinovávett on var? = z{ckstatoest...+ aco', +]
